Ratio & Proportion, Alligation or Mixture

PrepBank · পাতা ৫ / ১১ · ৪০১–৫০০ / ১,০৮৬

৪০১.

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is-

ক
4%
খ
6.25%
গ
20%
ঘ
25%

সঠিক উত্তর: গ

20%

উত্তর

সঠিক উত্তর: গ

20%

গ

ব্যাখ্যা

Question: A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is-

Solution:
Let C.P. of 1 litre milk be Tk. 1
Then,
S.P. of 1 litre of mixture = Tk. 1,
Gain = 25%.

C.P. of 1 litre mixture = Tk. (100/125) × 1 = Tk. 4/5

By the rule of alligation, we have:

⇒ Quantity of water : Quantity of milk = (1 - 4/5) : (4/5 - 0) = 1/5 : 4/5 = 1 : 4

Hence, percentage of water in the mixture = (1/5) × 100% = 20%

৪০২.

There are Tiger and peacock in zoo. The total number of their heads is 60 and the total number of their legs is 180. How many peacocks are there?

ক
35
খ
25
গ
40
ঘ
30

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: There are Tiger and peacock in zoo. The total number of their heads is 60 and the total number of their legs is 180. How many peacocks are there?

Solution:
Let,
There are x peacocks

So the number of tiger = (60 - x)

ATQ,
2x + 4(60 - x) = 180
⇒ 2x + 240 - 4x = 180
⇒ 240 - 2x = 180
⇒ 240 - 180 = 2x
⇒ 60 = 2x
⇒ x = 60/2
∴ x = 30

৪০৩.

Rahim and Karim started a business investing Tk. 26000 and Tk. 30000 respectively. Out of a total profit of Tk. 7000, Rahim's share is -

ক
Tk. 3050
খ
Tk. 3150
গ
Tk. 3250
ঘ
Tk. 3450

সঠিক উত্তর: গ

Tk. 3250

উত্তর

সঠিক উত্তর: গ

Tk. 3250

গ

ব্যাখ্যা

Question: Rahim and Karim started a business investing Tk. 26000 and Tk. 30000 respectively. Out of a total profit of Tk. 7000, Rahim's share is -

Solution:
Given,
Investment ratio = 26000 : 30000
= 13 : 15
Sum of the ratio's = 13 + 15 = 28

∴ Rahim's share = 7000 × (13/28)
= Tk. 3250

৪০৪.

A starts a business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

ক
ক) 7000 Tk
খ
খ) 9000 Tk
গ
গ) 8000 Tk
ঘ
ঘ) 12000 Tk

সঠিক উত্তর: খ

খ) 9000 Tk

উত্তর

সঠিক উত্তর: খ

খ) 9000 Tk

খ

ব্যাখ্যা

Question: A starts a business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

Solution:
Let B's capital be Tk x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x

Then,
(3500 × 12)/7x = 2/3
⇒ 14x = 126000
⇒ x = 9000

৪০৫.

The incomes of X and Y are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. If each of them saves Tk. 1000, then, X’s income can be

ক
Tk. 1000
খ
Tk. 2000
গ
Tk. 4000
ঘ
Tk. 6000

সঠিক উত্তর: ঘ

Tk. 6000

উত্তর

সঠিক উত্তর: ঘ

Tk. 6000

ঘ

ব্যাখ্যা

Question: The incomes of X and Y are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. If each of them saves Tk. 1000, then, X’s income can be

Solution:
The incomes of X and Y are 3x, 2x
their expenditures are 5y, 3y

3x - 5y = 1000
2x - 3y = 1000

3x - 5y = 2x - 3y
⇒ x = 2y

3 × 2y - 5y = 1000
⇒ y = 1000
x = 2 × 1000 = 2000 taka

∴ X’s income = 3x
= 3 × 2000
= Tk. 6000

৪০৬.

The ratio of the speeds of a train and a man 6 : 1 . The length of the train is 650 m and crosses a pole in 1 minute 5 seconds. In how much time will the man cross the 240 m long platform?

ক
ক) 1 min 24 sec
খ
খ) 2 min 30 sec
গ
গ) 2 min
ঘ
ঘ) 2 min 24 sec

সঠিক উত্তর: ঘ

ঘ) 2 min 24 sec

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2 min 24 sec

ঘ

ব্যাখ্যা

Speed of train = 650/65 = 10 m/s
Let, speed of the man is x
So, 6:1 = 10:x
∴ x = 10/6 = 5/3
Time required to cross the platform by the man = 240/(5/3) = 144 sec = 2 minutes 24 seconds

৪০৭.

A dishonest milkman professes to sell his milk at cost price but he mixes water with it and thereby gains 20%. The percentage of water in the mixture is:

ক
22.58%
খ
16.67%
গ
12.67%
ঘ
20.67%

সঠিক উত্তর: খ

16.67%

উত্তর

সঠিক উত্তর: খ

16.67%

খ

ব্যাখ্যা

Question: A dishonest milkman professes to sell his milk at cost price but he mixes water with it and thereby gains 20%. The percentage of water in the mixture is:

Solution:
let,
cost price = 100
sell price = 120

∴ the amount of milk = 100/120
= 5/6

∴ the amount of water is = (1 - 5/6) × 100%
= 16.67%

৪০৮.

If a : b = 3 : 4, b : c = 4 : 7, then (a + b + c)/c is equal to

ক
ক) 1
খ
খ) 2
গ
গ) 0
ঘ
ঘ) 3

সঠিক উত্তর: খ

খ) 2

উত্তর

সঠিক উত্তর: খ

খ) 2

খ

ব্যাখ্যা

a : b = 3 : 4
b : c = 4 : 7
a : b : c = 3 : 4 : 7

Let a = 3k,b = 4k, c = 7k

(a + b + c)/c = (3k + 4k + 7k)/7k
= 14k/7k
= 2

৪০৯.

Half of Taposh's investment in FDR is equal to one-third of his investment in National Savings Certificate. If he has Tk. 300000 as total investment, how much he invested in National Savings Certificate?

ক
ক) Tk. 120000
খ
খ) Tk. 180000
গ
গ) Tk. 150000
ঘ
ঘ) Tk. 200000

সঠিক উত্তর: খ

খ) Tk. 180000

উত্তর

সঠিক উত্তর: খ

খ) Tk. 180000

খ

ব্যাখ্যা

Question: Half of Taposh's investment in FDR is equal to one-third of his investment in National Savings Certificate. If he has Tk. 300000 as total investment, how much he invested in National Savings Certificate?

Solution:
Let,
Taposh invested in National Savings Certificate Tk. x
∴ He invested in FDR Tk. (300000 - x)

ATQ,
x/3 = (300000 - x)/2
⇒ 2x = 900000 - 3x
⇒ 5x = 900000
⇒ x = 900000/5
∴ x = 180000

∴ He invested Tk. 180000 in National Savings Certificate.

৪১০.

In a town, the ratio of the number of men to the number of women is 3 : 5. If 120 men and 80 women shift to the town, the new ratio of men to women becomes 2 : 3. What was the initial number of men in the town?

ক
480
খ
560
গ
600
ঘ
640
ঙ
710

সঠিক উত্তর: গ

600

উত্তর

সঠিক উত্তর: গ

600

গ

ব্যাখ্যা

Question: In a town, the ratio of the number of men to the number of women is 3 : 5. If 120 men and 80 women shift to the town, the new ratio of men to women becomes 2 : 3. What was the initial number of men in the town?

Solution:
Let the initial number of men and women be 3x and 5x, respectively.

According to the question,
(3x + 120)/(5x + 80) = 2/3
⇒ 3(3x + 120) = 2(5x + 80)
⇒ 9x + 360 = 10x + 160
⇒ 360 - 160 = 10x - 9x
⇒ 200 = x
∴ x = 200

∴ The initial number of men = 3x = 3(200)
= 600 men

৪১১.

3 varieties of wheat were mixed at a warehouse. The rate of Type 1 wheat was Tk 145 Kg and the rate of Type 2 wheat was Tk. 20 per kg more than Type 1. The quantities of 3 varieties of wheat were in the ratio 2 : 1 : 3 respectively. The mix was finally sold at the rate of Tk. 180 per kg. Find the price of the 3rd type of wheat?

ক
ক) Tk. 196.58
খ
খ) Tk. 208.33
গ
গ) Tk. 210
ঘ
ঘ) Tk. 215.67

সঠিক উত্তর: খ

খ) Tk. 208.33

উত্তর

সঠিক উত্তর: খ

খ) Tk. 208.33

খ

ব্যাখ্যা

Let the rate of 3^rd type of wheat be Tk. W
Quantity ratio = 2 : 1 : 3
This means if we take 2kg of Type 1 and 1 kg of Type 2, then we must take 3kg of Type 3.
Also, the mix will have 2kg + 1kg + 3kg = 6 kg quantity.
∴ (145 x 2) + (165 x 1) + (3 x W) = 6 x 180
⇒ 290 + 165 + 3W = 1080
⇒ 3W = 1080 - 455
⇒ 3W = 625
⇒ W = 625/3
⇒ W = 208.33

∴ W = Tk. 208.33 per kg = 3^rd type price per kg

৪১২.

A diamond’s value increases with the square of its mass. A 20-decigram gem costs 4800 tk. How much would an 8-decigram version of the same quality cost?

ক
468 tk
খ
672 tk
গ
732 tk
ঘ
768 tk

সঠিক উত্তর: ঘ

768 tk

উত্তর

সঠিক উত্তর: ঘ

768 tk

ঘ

ব্যাখ্যা

Question: A diamond’s value increases with the square of its mass. A 20-decigram gem costs 4800 tk. How much would an 8-decigram version of the same quality cost?

Solution:
Let's denote the weight of the diamond by w and the cost by C.
According to the problem,
C ∝ w²
⇒ c = k × w² [where k is a constant]
⇒ 4800 = k × 20²
⇒ k = 4800/400
∴ k = 12

Now, for w = 8 decigrams
C = 12 × 8²
∴ C = 768 tk

৪১৩.

The ratio of two numbers is 2 : 3 and their product is 726. The smallest number between the two numbers is-

ক
22
খ
33
গ
35
ঘ
28

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The ratio of two numbers is 2 : 3 and their product is 726. The smallest number between the two numbers is-

Solution:
Given that,
Ratio of two numbers is 2 : 3 and Their product is 726.

Let the numbers be 2n and 3n.

So according to the question :
⇒ 2n × 3n = 726
⇒ 6n² = 726
⇒ n² = 726/6
⇒ n² = 121
⇒ n = √121 [Ignoring the negative value]
∴ n = 11

Now,
Smaller number = 2n = 2 × 11 = 22
Larger number = 3n = 3 × 11 = 33

Therefore, Smaller number is 22.

৪১৪.

ক
8 : 6 : 12 : 9
খ
8 : 9 : 10 : 6
গ
9 : 6 : 10 : 8
ঘ
8 : 6 : 10 : 9
ঙ
None

সঠিক উত্তর: ঘ

8 : 6 : 10 : 9

উত্তর

সঠিক উত্তর: ঘ

8 : 6 : 10 : 9

ঘ

ব্যাখ্যা

A : B = 1/2 : 3/8 = 4 : 3 = 8 : 6
B : C = 1/3 : 5/9 = 3 : 5 = 6 : 10
C : D = 5/6 : 3/4 = 10 : 9
A : B : C : D = 8 : 6 : 10 : 9
-----------------------------------
Alternative way:

A : B = 1/2 : 3/8
= (1 × 8)/2 : (3 × 8) /8
= 4 : 3
= 8 : 6
B : C = 1/3 : 5/9
= (1 × 9)/3 : (5 × 9)/9
= 3 : 5
= (3 × 2) : (5 × 2)
= 6 : 10
C : D = 5/6 : 3/4
= (5 × 12) /6 : (3 × 12)/4
= 10 : 9
A : B : C : D = 8 : 6 : 10 : 9

৪১৫.

In a mixture of 50 liters milk and water are in the ratio of 3 : 2. How much water should be added to the mixture to make the ratio of the two equal?

ক
14 liters
খ
12 liters
গ
10 liters
ঘ
8 liters

সঠিক উত্তর: গ

10 liters

উত্তর

সঠিক উত্তর: গ

10 liters

গ

ব্যাখ্যা

Question: In a mixture of 50 litres milk and water are in the ratio of 3 : 2. How much water should be added to the mixture to make the ratio of the two equal?

Solution:
Amount of milk = (3 × 50)/5
= 30 liters
Amount of water = 50 - 30 litre
= 20 liters

water to be added = 30 - 20 litre
= 10 liters

৪১৬.

The students in three batches in school is in the ratio of 2 : 3 : 5. If 20 students in each batch are increased than the ratio changes to 4 : 5 : 7. The total number of students in the three before the increase was-

ক
150
খ
100
গ
90
ঘ
10

সঠিক উত্তর: খ

100

উত্তর

সঠিক উত্তর: খ

100

খ

ব্যাখ্যা

Question: The students in three batches in school is in the ratio of 2 : 3 : 5. If 20 students in each batch are increased than the ratio changes to 4 : 5 : 7. The total number of students in the three before the increase was-

Solution:
Let, students in the three before the increase were 2x, 3x, 5x

After increase, 2x + 20, 3x + 20, 5x + 20

(2x + 20)/ (3x + 20) = 4/5
⇒ 10x + 100 = 12x + 80
⇒ 2x = 20
⇒ x = 10

The total number of students in the three before the increase was = (2x + 5x + 3x)
= 10x
= 10 × 10
= 100

৪১৭.

The sum of the squares of three numbers is 532 and the ratio of the first and the second as also of the second and the third is 3 : 2. The third number is -

ক
8
খ
12
গ
28
ঘ
25
ঙ
40

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The sum of the squares of three numbers is 532 and the ratio of the first and the second as also of the second and the third is 3 : 2. The third number is -

Solution:
Given that,
First : Second = 3 : 2
Second : third = 3 : 2
= {3 × (2/3)} : {2 × (2/3)}
= 2 : (4/3)

∴ Ratio between the numbers = 3 : 2 : (4/3)
= 9 : 6 : 4
Let the numbers be 9x, 6x and 4x
Then,
⇒ (9x)² + (6x)² + (4x)² = 532
⇒ 81x² + 36x² + 16x² = 532
⇒ 133x² = 532
⇒ x² = 4
⇒ x = 2

So, third number = 4x = 4 × 2 = 8

৪১৮.

A and B are two alloys in which the ratios of gold and copper are 5 : 3 and 5 : 11 respectively. If these equal amounts of two alloys are melted and made into alloy C. What will be the ratio of gold and copper in alloy C?

ক
3 : 5
খ
5 : 11
গ
7 : 15
ঘ
15 : 17

সঠিক উত্তর: ঘ

15 : 17

উত্তর

সঠিক উত্তর: ঘ

15 : 17

ঘ

ব্যাখ্যা

Question: A and B are two alloys in which the ratios of gold and copper are 5 : 3 and 5 : 11 respectively. If these equal amounts of two alloys are melted and made into alloy C. What will be the ratio of gold and copper in alloy C?

Solution:
Ratio of Gold and Copper in Alloy A = 5 : 3
Ratio of Gold and Copper in Alloy B = 5 : 11

Amount of Gold in Alloy A = 5/8
Amount of Gold In Alloy B = 5/16

Amount of Copper in A = 3/8
Amount of Copper in B = 11/16

∴ Amount of Gold In C = Amount of gold in A + Amount of gold in B
= (5/8) + (5/16)
= (10 + 5)/16
= 15/16

∴ Amount of Copper in C = Amount of Copper in A + Amount of Copper in B
= (3/8) + (11/16)
= (6 + 11)/16
= 17/16

∴ Ratio of Gold and Copper in C = (15/16) : (17/16)
= 15 : 17

৪১৯.

To gain 25% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is-

ক
12.5 kg
খ
10 kg
গ
8.5 kg
ঘ
9 kg

সঠিক উত্তর: ক

12.5 kg

উত্তর

সঠিক উত্তর: ক

12.5 kg

ক

ব্যাখ্যা

Question: To gain 25% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

Solution:
Let the quantity of water mixed be x kg
Let CP of 1 kg of pure milk = Tk 1

Hence,
% gain = x × (100/50)
⇒ 25 = 100x/50
⇒ 100x = 1250
∴ x = 12.5

৪২০.

In a sugar-water solution, the ratio of water to sugar is 8 : 3. If you add 2 kgs of sugar, the ratio becomes 2 : 1. What is the amount of sugar in the original solution in kg?

ক
ক) 3
খ
খ) 4.5
গ
গ) 6
ঘ
ঘ) 8

সঠিক উত্তর: গ

গ) 6

উত্তর

সঠিক উত্তর: গ

গ) 6

গ

ব্যাখ্যা

Let
amount of water be 8x.
So, the amount of sugar is 3x.
According to question,
8x/(3x + 2) = 2/1
Solving this equation, we get, x = 2
Therefore, the amount of sugar in the original solution = 3 × 2 = 6 kg.

৪২১.

An amount of Tk. 735 was divided between A, B and C. If each of them had received Tk. 25 less, their shares would have been in the ratio of 1 : 3 : 2. The money received by C was :

ক
ক) 195
খ
খ) 200
গ
গ) 225
ঘ
ঘ) 245

সঠিক উত্তর: ঘ

ঘ) 245

উত্তর

সঠিক উত্তর: ঘ

ঘ) 245

ঘ

ব্যাখ্যা

ধরি,
A. পায় (x - 25) টাকা,
B পায় (3x - 25) টাকা
C পায় (2x - 25) টাকা।
প্রশ্নমতে,
(x - 25) + (3x - 25) + (2x - 25) = 735
6x - 75 = 735
6x = 735 + 75
6x = 810
x = 135

C পায় = 2x - 25 টাকা
= (2 × 135 - 25) টাকা
= 245 টাকা

৪২২.

An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 17 minutes. What is the ratio of lunch breaks to the total period in the office?

ক
1 : 30
খ
1 : 17
গ
3 : 10
ঘ
5 : 27

সঠিক উত্তর: ক

1 : 30

উত্তর

সঠিক উত্তর: ক

1 : 30

ক

ব্যাখ্যা

Question: An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 17 minutes. What is the ratio of lunch breaks to the total period in the office?

Solution:
The ratio of lunch breaks to the total period in the office = 17/{(8 × 60) + 30}
= 17/510
= 1/30
= 1 : 30

৪২৩.

There are 130 mangoes and guavas in a basket and their ratio is 3 : 2 respectively. To make the ratio of mango and guava 1 : 1 in that basket, how many new fruits should be added?

ক
২৬
খ
২১
গ
২২
ঘ
৩০
ঙ
৩২

সঠিক উত্তর: ক

২৬

উত্তর

সঠিক উত্তর: ক

২৬

ক

ব্যাখ্যা

আম ও পেয়ারার অনুপাত = ৩:২
তাহলে আম আছে = ১৩০ এর ৩/ ৫ = ৭৮ টি
পেয়ারা আছে = ১৩০ এর ২/৫ = ৫২ টি
তাহলে অনুপাত ১:১ হতে হলে নতুন পেয়ারা যোগ করতে হবে = ৭৮-৫২ = ২৬ টি

৪২৪.

Poltu divided one-third of his money in a 2 : 3 ratio between Ratul and Shovon, and the remainder in the same ratio between Nitul and Sanhar. If Sanhar received 360 Tk, what was Poltu's total amount?

ক
1800 Tk
খ
600 Tk
গ
900 Tk
ঘ
1500 Tk

সঠিক উত্তর: গ

900 Tk

উত্তর

সঠিক উত্তর: গ

900 Tk

গ

ব্যাখ্যা

Question: Poltu divided one-third of his money in a 2 : 3 ratio between Ratul and Shovon, and the remainder in the same ratio between Nitul and Sanhar. If Sanhar received 360 Tk, what was Poltu's total amount?

Solution:
If Sanhar received 360 Tk,
Nitul received = (360/3) × 2 Tk
= 240 Tk

Total amount Nitul and Sanhar received = 360 + 240 Tk
= 600 Tk [which is {1 - (1/3)} or 2/3 of total amount]

∴ Total amount = (600/2) × 3 Tk
= 900 Tk

৪২৫.

Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves Tk. 300 per week, find their weekly incomes.

ক
Tk. 6000 and Tk. 2500
খ
Tk. 6300 and Tk. 2700
গ
Tk. 6500 and Tk. 2800
ঘ
Tk. 6200 and Tk. 2600
ঙ
None of these

সঠিক উত্তর: খ

Tk. 6300 and Tk. 2700

উত্তর

সঠিক উত্তর: খ

Tk. 6300 and Tk. 2700

খ

ব্যাখ্যা

Question: Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves Tk. 300 per week, find their weekly incomes.

Solution:
Let the incomes of the two persons be 7x and 3x
And their expenses be 5y and 2y respectively.

Then we get,
7x - 5y = 3x - 2y
⇒ 4x = 3y
∴ y = 4x/3

Now, 7x - 5y = 300
⇒ 7x - 5(4x/3) = 300
⇒ (21x - 20x)/3 = 300
∴ x = Tk. 900

∴ Weekly income of first person = (7 × 900) = Tk. 6300
∴ Weekly income of second person = (3 × 900) = Tk. 2700

So weekly incomes are Tk. 6300 and Tk. 2700

৪২৬.

Gold is 17 times as heavy as water and copper is 8 times as heavy as water. In what ratio should these be mixed to get an alloy 13 times as heavy as water?

ক
ক) 3 : 2
খ
খ) 5 : 4
গ
গ) 6 : 7
ঘ
ঘ) 8 : 5

সঠিক উত্তর: খ

খ) 5 : 4

উত্তর

সঠিক উত্তর: খ

খ) 5 : 4

খ

ব্যাখ্যা

Question: Gold is 17 times as heavy as water and copper is 8 times as heavy as water. In what ratio should these be mixed to get an alloy 13 times as heavy as water?

Solution:
Let, gold is 17x times as heavy as water and copper is 8y times as heavy as water.

ATQ,
17x + 8y = 13(x + y)
⇒ 17x + 8y = 13x + 13y
⇒ 17x - 13x = 13y - 8y
⇒ 4x = 5y
⇒ x/y = 5/4
∴ x : y = 5 : 4

৪২৭.

A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4 : 5. Find the quantity of alcohol in the given mixture.

ক
10 litres
খ
12 litres
গ
15 litres
ঘ
18 litres

সঠিক উত্তর: ক

10 litres

উত্তর

সঠিক উত্তর: ক

10 litres

ক

ব্যাখ্যা

Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4 : 5. Find the quantity of alcohol in the given mixture.

Solution:

Let the quantity of alcohol and water be 4x litres and 3x litres respectively

ATQ,
4x/(3x + 5) = 4/5

⇒ 20x = 4(3x + 5)
⇒ 20x = 12x + 20

⇒ 8x = 20

∴ x = 2.5

Quantity of alcohol = (4 × 2.5) litres = 10 litres.

৪২৮.

A hospital uses a mixture of salt and water at Tk. 7.62/litre. This mixture contains 5% salt. Another mixture containing 75% water costs Tk. 7.82/litre. How much does the patient pay if he buys 5 litres of mixture containing 18% salt?

ক
Tk. 83.75
খ
Tk. 73.85
গ
Tk. 37.85
ঘ
Tk. 38.75

সঠিক উত্তর: ঘ

Tk. 38.75

উত্তর

সঠিক উত্তর: ঘ

Tk. 38.75

ঘ

ব্যাখ্যা

Question: A hospital uses a mixture of salt and water at Tk. 7.62/litre. This mixture contains 5% salt. Another mixture containing 75% water costs Tk. 7.82/litre. How much does the patient pay if he buys 5 litres of mixture containing 18% salt?

Solution:
1st mixture contains 5% salt.
2nd mixture contains 75% water i.e. 25 % salt.
Required % of salt = 18%.
∴ Required ratio = 25 - 18 : 18 - 5 = 7 : 13
and required price of the mixture = 7.82 - x : x - 7.62 = 7 : 13 [Let, patient pays Tk. x per kg]
⇒ 13(7.82 - x) = 7(x - 7.62)
⇒ 101.66 - 13x = 7x - 53.34
⇒ 20x = 155
⇒ x = 7.75
Hence price of 5 liters of this mixture = 7.75 × 5 = Tk. 38.75.

৪২৯.

A bag contains red, blue, and green balls in the ratio 3 : 5 : 7. If there are 45 blue balls, how many total balls are there in the bag?

ক
90
খ
105
গ
120
ঘ
135

সঠিক উত্তর: ঘ

135

উত্তর

সঠিক উত্তর: ঘ

135

ঘ

ব্যাখ্যা

Question: A bag contains red, blue, and green balls in the ratio 3 : 5 : 7. If there are 45 blue balls, how many total balls are there in the bag?

Solution: Given ratio = Red : Blue : Green = 3 : 5 : 7
Let the numbers be:
Red = 3x, Blue = 5x, Green = 7x

Given:
5x = 45
⇒ x = 45 ÷ 5 = 9

Now calculate total balls:
= 3x + 5x + 7x
= (3 + 5 + 7)x = 15x
= 15 × 9 = 135

৪৩০.

If p : q = 7 : 3, then the value of 5p + 70 : 3q + 18 is

ক
30 : 7
খ
35 : 9
গ
25 : 9
ঘ
None of these

সঠিক উত্তর: খ

35 : 9

উত্তর

সঠিক উত্তর: খ

35 : 9

খ

ব্যাখ্যা

p : q = 7 : 3
or, p/q = 7/3
or, 5p/3q = (5 × 7)/(3 × 3)
or, 5p/3q = 35/9
or, 5p/35 = 3q/9
or, (5p + 70)/35 = (3q + 18)/9
or, (5p + 70)/(3q + 18) = 35/9
or, (5p + 70) : (3q + 18) = 35 : 9
---------------------------------
Short-cut
p = 7, q = 3
5p + 70 : 3q + 18 = 5 × 7 + 70 : 3 × 3 + 18 = 105 : 27 = 35 : 9

৪৩১.

Three boys have marbles in the ratio of 19 : 5 : 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the highest number have?

ক
ক) 57
খ
খ) 15
গ
গ) 76
ঘ
ঘ) 38

সঠিক উত্তর: ক

ক) 57

উত্তর

সঠিক উত্তর: ক

ক) 57

ক

ব্যাখ্যা

Question: Three boys have marbles in the ratio of 19 : 5 : 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the highest number have?

Solution:
ধরি,
তিন জনের মারবেলের পরিমান যথাক্রমে 19x, 5x, 3x

প্রশ্নমতে,
3x = 9
x = 3

প্রথম জনের মারবেল / সর্বোচ্চ মারবেল = 19x
= 19 × 3
= 57

৪৩২.

If a : b = 4 : 7 and b : c = 5 : 6 than a : b : c = ?

ক
ক) 8 : 15 : 12
খ
খ) 20 : 35 : 42
গ
গ) 20 : 35 : 24
ঘ
ঘ) None

সঠিক উত্তর: খ

খ) 20 : 35 : 42

উত্তর

সঠিক উত্তর: খ

খ) 20 : 35 : 42

খ

ব্যাখ্যা

Question: If a : b = 4 : 7 and b : c = 5 : 6 than a : b : c = ?

Solution:
a : b = 4 : 7 = 20 : 35
b : c = 5 : 6 = 35 : 42

a : b : c = 20 : 35 : 42

৪৩৩.

What must be added to each term of the ratio 7 : 11 so as to make it equal to 5 : 6?

ক
ক) 9
খ
খ) 11
গ
গ) 13
ঘ
ঘ) 17

সঠিক উত্তর: গ

গ) 13

উত্তর

সঠিক উত্তর: গ

গ) 13

গ

ব্যাখ্যা

Question: What must be added to each term of the ratio 7 : 11 so as to make it equal to 5 : 6?

Solution:
let, the number be x

(7 + x) : (11 + x) = 5 : 6
⇒ (7 + x) / (11 + x) = 5/6
⇒ 6 (7 + x) = 5 (11 + x)
⇒ 42 + 6x = 55 + 5x
⇒ 6x - 5x = 55 - 42
∴ x = 13

৪৩৪.

The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square?

ক
5 : 18
খ
14 : 5
গ
16 : 5
ঘ
32 : 5

সঠিক উত্তর: গ

16 : 5

উত্তর

সঠিক উত্তর: গ

16 : 5

গ

ব্যাখ্যা

Question: The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square?

Solution:
Let,
Arm of the square be a cm.
Area of square = 1024 sq.cm.
∴ a² = 1024
⇒ a = √1024
∴ a = 32

Length of rectangle = 2a = (2 × 32) cm = 64 cm.
Breadth of rectangle = (32 - 12) cm = 20 cm.

∴ Required ratio = 64 : 20 = 16 : 5.

৪৩৫.

The cost of variety A wheat flour is Tk. 42 per kg and variety B wheat flour is Tk. 35 per kg. If both variety A and variety B are mixed in the ratio of 3 : 2, then the price per kg of the mixed variety of wheat flour is:

ক
Tk. 37.40
খ
Tk. 39.20
গ
Tk. 38.50
ঘ
Tk. 41.50

সঠিক উত্তর: খ

Tk. 39.20

উত্তর

সঠিক উত্তর: খ

Tk. 39.20

খ

ব্যাখ্যা

Question: The cost of variety A wheat flour is Tk. 42 per kg and variety B wheat flour is Tk. 35 per kg. If both variety A and variety B are mixed in the ratio of 3 : 2, then the price per kg of the mixed variety of wheat flour is:

Solution:
Let,
Quantity of variety A flour is 3x kg.
Quantity of variety B flour is 2x kg.
The price per kg of the mixed variety of flour is y taka
∴ Total price of variety A flour is 42 × 3x = 126x Taka
∴ Total price of variety B flour is 35 × 2x = 70x Taka

ATQ,
126x + 70x = y(3x + 2x)
⇒ 196x = y × 5x
⇒ y = (196x)/(5x)
∴ y = 39.2
Therefore, the price per kg of the mixed variety of wheat flour is Tk. 39.20

৪৩৬.

David got two and a half time as many marks in English as in History. If his total marks in the two subjects are 140, the marks obtained by him in English are:

ক
40
খ
75
গ
90
ঘ
100

সঠিক উত্তর: ঘ

100

উত্তর

সঠিক উত্তর: ঘ

100

ঘ

ব্যাখ্যা

Question: David got two and a half time as many marks in English as in History. If his total marks in the two subjects are 140, the marks obtained by him in English are:

Solution:
Let,
The marks of History = x
∴ The marks of English = 2.5x

ATQ,
x + 2.5x = 140
⇒ 3.5x = 140
⇒ x = 140/3.5
∴ x = 40

∴ The marks of English = 2.5x = 2.5 × 40 = 100

৪৩৭.

The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers?

ক
28
খ
32
গ
26
ঘ
30

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers?

Solution:
Let two positive numbers be 3x and 4x.
ATQ,
(3x)² + (4x)² = 400
⇒ 9x² + 16x² = 400
⇒ 25x² = 400
⇒ x² = 400/25
⇒ x²= 16
∴ x = 4

Sum of numbers = (3 × 4) + (4 × 4) = 28

৪৩৮.

Abu and Salim started a partnership business investing some amount of money in the ratio of 4 : 6. Shakeel joined them after six months with an amount equal to that of Salim. In what proportion should the profit at the end of one year be distributed among Abu, Salim and Shakeel?

ক
5 : 3 : 4
খ
4 : 6 : 2
গ
5 : 3 : 2
ঘ
4 : 6 : 3

সঠিক উত্তর: ঘ

4 : 6 : 3

উত্তর

সঠিক উত্তর: ঘ

4 : 6 : 3

ঘ

ব্যাখ্যা

Question: Abu and Salim started a partnership business investing some amount of money in the ratio of 4 : 6. Shakeel joined them after six months with an amount equal to that of Salim. In what proportion should the profit at the end of one year be distributed among Abu, Salim and Shakeel?

Solution:
As (4 : 6 is equivalent to 2 : 3)
So let the initial investment of money ratio of Abu and Salim is 2x and 3x.
So Abu , Salim and Shakeel ratio of investment will be ( Abu : Salim : Shakeel ) = (2x × 12) : (3x × 12) : (3x × 6) = 24 : 36 : 18 = 4 : 6 : 3

৪৩৯.

A, B and C start a business. A invests 3 times as much as B invests 2/3rd as much as C invests. Find the ratio of capitals of A, B and C ?

ক
ক) 6 : 2 : 3
খ
খ) 5 : 2 : 10
গ
গ) 6 : 10 : 3
ঘ
ঘ) 12 : 3 : 2

সঠিক উত্তর: ক

ক) 6 : 2 : 3

উত্তর

সঠিক উত্তর: ক

ক) 6 : 2 : 3

ক

ব্যাখ্যা

Question: A, B and C start a business. A invests 3 times as much as B invests 2/3rd as much as C invests. Find the ratio of capitals of A, B and C ?

Solution:
ধরি
C বিনিয়োগ করে = x টাকা
B বিনিয়োগ করে = 2x/3 টাকা
A বিনিয়োগ করে = 3× (2x/3) টাকা
= 2x টাকা
A, B এবং C এর বিনিয়োগের অনুপাত = 2x : (2x/3) : x
= 2 : (2/3) : 1
= 6 : 2 : 3

৪৪০.

If a and b are integers greater than 200 such that a + b = 600, which of the following could be the exact ratio of a to b?

ক
ক) 3 to 2
খ
খ) 5 to 2
গ
গ) 7 to 3
ঘ
ঘ) 9 to 1

সঠিক উত্তর: ক

ক) 3 to 2

উত্তর

সঠিক উত্তর: ক

ক) 3 to 2

ক

ব্যাখ্যা

for, 3 to 2,
600 × 3/(3 + 2) = 360; which is greater than 200. This maybe the correct answer.

for, 5 to 2,
600 × 2/(5 + 2) = 171.43; which is less than 200. This is not the correct answer.

for, 7 to 3,
600 × 3/(7 + 3) = 180; which is less than 200. This is not the correct answer.

for, 9 to 1,
600 × 1/(9 + 1) = 60; which is less than 200. This is not the correct answer.

৪৪১.

If A : B = 2 : 3, B : C = 4 : 5, C : D = 5 : 9 then A : D = ?

ক
ক) 11 : 17
খ
খ) 8 : 27
গ
গ) 5 : 9
ঘ
ঘ) 2 : 9
ঙ
ঙ) 9 : 2

সঠিক উত্তর: খ

খ) 8 : 27

উত্তর

সঠিক উত্তর: খ

খ) 8 : 27

খ

ব্যাখ্যা

A/D = (A/(B × B))/((C × C)/D)
= (2/(3 × 4))/((5 × 5)/9)
= (2 × 4 × 5)/(3 × 5 × 9)
= 8/27
= 8 : 27

৪৪২.

The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?

ক
12 : 5
খ
12 : 7
গ
10 : 7
ঘ
13 : 6

সঠিক উত্তর: ক

12 : 5

উত্তর

সঠিক উত্তর: ক

12 : 5

ক

ব্যাখ্যা

Question: The ratio of the present ages of a mother and son is 7 : 2. After 7 years, the ratio of their ages becomes 8 : 3. What will be the ratio of their ages after 11 years?

Solution:
Let,
The present age of the mother = 7x years
The present age of the son = 2x years

After 7 years, their ages will be:
Mother = (7x + 7) years
Son = (2x + 7) years

According to the question,
(7x + 7)/(2x + 7) = 8/3
⇒ 3(7x + 7) = 8(2x + 7)
⇒ 21x + 21 = 16x + 56
⇒ 21x - 16x = 56 - 21
⇒ 5x = 35
⇒ x = 35/5
∴ x = 7

Present age of mother = 7 × 7 = 49 years
Present age of son = 2 × 7 = 14 years

Now, after 11 years,
Mother's age = 49 + 11 = 60 years
Son's age = 14 + 11 = 25 years

∴ The ratio of their ages after 11 years,
= 60 : 25
= 12 : 5

৪৪৩.

In a football match 30000 tickets have been sold. One-fourth of the tickets has been sold at Tk. 30 each, One-third has been sold at Tk. 25 each, and the remaining tickets have been sold at Tk. 20 each. What is total amount of selling price?

ক
ক) 725000 Tk.
খ
খ) 750000 Tk.
গ
গ) 775000 Tk.
ঘ
ঘ) 765000 Tk.

সঠিক উত্তর: ক

ক) 725000 Tk.

উত্তর

সঠিক উত্তর: ক

ক) 725000 Tk.

ক

ব্যাখ্যা

Question: In a football match 30000 tickets have been sold. One-fourth of the tickets has been sold at Tk. 30 each, One-third has been sold at Tk. 25 each, and the remaining tickets have been sold at Tk. 20 each. What is total amount of selling price?

Solution:
One- fourth of 30000 is = 30000 × (1/4) = 7500
∴ The price of 7500 tickets at Tk. 30 each = (7500 × 30) = 225000 Tk.

One-third of 30000 is = 30000 × (1/3) = 10000
∴ The price of 10000 tickets at Tk. 25 each = (10000 × 25) = 250000 Tk.

Remaining tickets = (30000 - 7500 - 10000) = 12500
∴ The price of 12500 tickets at Tk. 20 each = (12500 × 20) = 250000 Tk.

Total amount of selling price = (225000 + 250000 + 250000) Tk.
= 725000 Tk.

৪৪৪.

The first, second and third terms of the proportion are 42, 36, 35. Find the fourth term.

ক
50
খ
40
গ
37
ঘ
32
ঙ
30

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Question: The first, second and third terms of the proportion are 42, 36, 35. Find the fourth term.

Solution:
Let the fourth term be x.

Thus 42, 36, 35, x are in proportion.
Product of extreme terms = 42 × x
Product of mean terms = 36 × 35

Since, the numbers make up a proportion
Therefore,
42 × x = 36 × 35
or, x = (36 × 35)/42
or, x = 30

Therefore, the fourth term of the proportion is 30.

৪৪৫.

The present ages of three persons are in the ratio of 4 : 7 : 9. Six years ago, the sum of their ages was 62. What was the age of the oldest person six years ago?

ক
36 years
খ
30 years
গ
28 years
ঘ
21 years
ঙ
16 years

সঠিক উত্তর: খ

30 years

উত্তর

সঠিক উত্তর: খ

30 years

খ

ব্যাখ্যা

Question: The present ages of three persons are in the ratio of 4 : 7 : 9. Six years ago, the sum of their ages was 62. What was the age of the oldest person six years ago?

Solution:
Let their present ages are 4x, 7x and 9x years respectively.
∴ 6 years ago, their present ages are (4x - 6), (7x - 6) and (9x - 6) respectively.

ATQ,
(4x - 6) + (7x - 6) + (9x - 6) = 62
⇒ 20x - 18 = 62
⇒ 20x = 62 + 18
⇒ x = 80/20
⇒ x = 4

∴ Their present ages are (4 × 4) =16, (7 × 4) = 28 and (9 × 4) = 36 years respectively.
∴ Age of the oldest person six years ago is (36 - 6) = 30 years.

৪৪৬.

If x : y = 5 : 3, then (11x + 2y) : (11x - 2y) = ?

ক
ক) 67 : 49
খ
খ) 57 : 43
গ
গ) 57 : 49
ঘ
ঘ) 61 : 49

সঠিক উত্তর: ঘ

ঘ) 61 : 49

উত্তর

সঠিক উত্তর: ঘ

ঘ) 61 : 49

ঘ

ব্যাখ্যা

x : y = 5 : 3
⇒ x/y = 5/3
⇒ 11x/2y = (11 × 5)/(2 × 3)
⇒ 11x/2y = 55/6
⇒ (11x + 2y)/(11x - 2y) = (55 + 6)/(55 - 6)
⇒ (11x + 2y)/(11x - 2y) = 61/49
⇒ (11x + 2y) : (11x - 2y) = 61 : 49

৪৪৭.

Five litres of wine is removed from a cask full of wine and is replaced with water. Five litres of this mixture is then removed and replaced with water. If the ratio of wine to water in the cask is now 16 : 9, how much wine did the cask hold?

ক
25 litres
খ
50 litres
গ
100 litres
ঘ
150 litres

সঠিক উত্তর: ক

25 litres

উত্তর

সঠিক উত্তর: ক

25 litres

ক

ব্যাখ্যা

Question: Five litres of wine is removed from a cask full of wine and is replaced with water. Five litres of this mixture is then removed and replaced with water. If the ratio of wine to water in the cask is now 16 : 9, how much wine did the cask hold?

Solution:
Let the cask holds x liters of wine.
5 liters of wine is replaced with water. This operation is done 2 times.
∴ [(x - 5)/x]² = 16/(16 + 9)
⇒ [(x - 5) / x]² = 16/25
⇒ [(x - 5)/x] = 4/5
⇒ 5x - 25 = 4x
⇒ x = 25 liters

৪৪৮.

If 2A = 3B = 4C, Than, A : B : C is.

ক
2 : 3 : 4
খ
4 : 3 : 2
গ
6 : 4 : 3
ঘ
20 : 15 : 2

সঠিক উত্তর: গ

6 : 4 : 3

উত্তর

সঠিক উত্তর: গ

6 : 4 : 3

গ

ব্যাখ্যা

Question: If 2A = 3B = 4C, Than, A : B : C is.

Solution:
Let
2A = 3B = 4C = x
2A = x
A = x/2

3B =x
B = x/3

4C = x
C = x/4

A : B : C = x/2 : x/3 : x/4
= (x/2) × 12 : (x/3) × 12 : (x/4) × 12
= 6 : 4 : 3

৪৪৯.

How many kg of custard powder costing Tk. 42 per kg must be mixed with 16 kg of custard powder costing Tk. 60 per kg so that 20 % may be gained by selling the mixture at Tk. 60 per kg?

ক
11 kg
খ
14 kg
গ
12 kg
ঘ
20 kg

সঠিক উত্তর: ঘ

20 kg

উত্তর

সঠিক উত্তর: ঘ

20 kg

ঘ

ব্যাখ্যা

Question: How many kg of custard powder costing Tk. 42 per kg must be mixed with 16 kg of custard powder costing Tk. 60 per kg so that 20 % may be gained by selling the mixture at Tk. 60 per kg?

Solution:
SP = 60.
Gain= 20%.
CP = (100/120) × 60.
∴ CP = 50.

Ratio between the 2 varieties of custard powder = 60 - 50 : 50 - 42 = 10 : 8.

∴ if x is the required quantity then 10 : 8 = x : 16
⇒ x = 20 kg.

৪৫০.

Let the ratio of x to y be a/b : - b/a, and if (x - y) = (a/b + b/a), it follows that x is equal to:

ক
- a/b
খ
a/b
গ
(a - b)/a
ঘ
None of the above

সঠিক উত্তর: খ

a/b

উত্তর

সঠিক উত্তর: খ

a/b

খ

ব্যাখ্যা

Question: Let the ratio of x to y be a/b : - b/a, and if (x - y) = (a/b + b/a), it follows that x is equal to:

Solution:
Given,
⇒ x/y =(a/b)/(-b/a)
⇒ x/y = - a²/b²
⇒ y =(−b²/a²)x

Now,
x - y = a/b + b/a
⇒ x + (b²/a²)x = (a² + b²)/ab
⇒ x(a² + b²)/a² = (a²+b²)/ab
⇒ x = a²/ab
⇒ x = a/b

৪৫১.

When 40% of the first number is added to the second number, the second number becomes 7/5 times the first number. What is the ratio of the first number to the second number?

ক
1 : 1
খ
2 : 3
গ
3 : 4
ঘ
3 : 8

সঠিক উত্তর: ক

1 : 1

উত্তর

সঠিক উত্তর: ক

1 : 1

ক

ব্যাখ্যা

Question: When 40% of the first number is added to the second number, the second number becomes 7/5 times the first number. What is the ratio of the first number to the second number?

Solution:
Let the first number = x
and the second number = y.

According to the question,
y + 40% of x = (7/5)x
⇒ y + (40/100) x = (7/5)x
⇒ y + (4/10)x = (7/5)x
⇒ y = (7/5)x - (4/10)x
⇒ y = (14 - 4)x/10
⇒ y = 10x/10
⇒ y = x

Therefore, x : y = x : x = 1 : 1

৪৫২.

In a selection process, the ratio of applicants who were selected to those who were rejected is 10 : 4. If 420 applicants were rejected, what was the total number of applicants?

ক
1400
খ
1520
গ
1620
ঘ
1470

সঠিক উত্তর: ঘ

1470

উত্তর

সঠিক উত্তর: ঘ

1470

ঘ

ব্যাখ্যা

Question: In a selection process, the ratio of applicants who were selected to those who were rejected is 10 : 4. If 420 applicants were rejected, what was the total number of applicants?

Solution:
Given ratio,
Selected : Rejected = 10 : 4
This means for every 10 selected applicants, 4 are rejected.

Let, Number of selected applicants = 10k
Number of rejected applicants = 4k

According to the question,
Rejected applicants = 420
So, 4k = 420
⇒ k = 420/4
∴ k = 105

∴ Selected applicants = 10k = 10 × 105 = 1050
∴ Rejected applicants = 4k = 420 (given)

∴ Total number of applicants = Selected + Rejected
= 1050 + 420
= 1470

So the total number of applicants was 1470.

৪৫৩.

An alloy contains Copper, Zinc and Nickel in the ratio of 5 : 3 : 2. The quantity of Nickel that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is-

ক
10 kg
খ
14 kg
গ
16 kg
ঘ
20 kg

সঠিক উত্তর: ক

10 kg

উত্তর

সঠিক উত্তর: ক

10 kg

ক

ব্যাখ্যা

Question: An alloy contains Copper, Zinc and Nickel in the ratio of 5 : 3 : 2. The quantity of Nickel that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is-

Solution:
Given that,
An alloy contains Copper : Zinc : Nickel = 5 : 3 : 2
Total weight = 100 kg

Now, Sum of the ratio, 5 + 3 + 2 = 10
Copper = (

kg
Zinc = (3/10)

kg
Nickel = (2/10)

kg

Now, Let the amount of Nickel to be added be x kg
Then, new quantity of Nickel =

Nickel that must be added 10 kg.

৪৫৪.

When 20% of a number is added to another number, the second number increased by 150%. What is the ratio between the first and the second number?

ক
2 : 15
খ
15 : 2
গ
15 : 1
ঘ
1 : 15

সঠিক উত্তর: খ

15 : 2

উত্তর

সঠিক উত্তর: খ

15 : 2

খ

ব্যাখ্যা

Question: When 20% of a number is added to another number, the second number increased by 150%. What is the ratio between the first and the second number?

Solution:
Let,
The numbers be X and Y

ATQ,
Y + 20% of X = Y + 150% of Y
⇒ 20X/100 = 150Y/100
⇒ 20X = 150Y
⇒ X/Y = 150/20
∴ X : Y = 15 : 2

৪৫৫.

In what ratio must two kinds of sugar at Tk. 115 and Tk. 124 per kg be mixed so that by selling at Tk. 150 per kg, 25% may be gained?

ক
4 : 5
খ
5 : 3
গ
1 : 1
ঘ
2 : 3

সঠিক উত্তর: ক

4 : 5

উত্তর

সঠিক উত্তর: ক

4 : 5

ক

ব্যাখ্যা

Question: In what ratio must two kinds of sugar at Tk. 115 and Tk. 124 per kg be mixed so that by selling at Tk. 150 per kg, 25% may be gained?

Solution:
SP = 150
Profit = 25%.
∴ CP = 150 × (100/125) = 120

Therefore required ratio = 4 : 5

৪৫৬.

To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is -

ক
ক) 2.5 kg
খ
খ) 5 kg
গ
গ) 7.5 kg
ঘ
ঘ) 10 kg

সঠিক উত্তর: খ

খ) 5 kg

উত্তর

সঠিক উত্তর: খ

খ) 5 kg

খ

ব্যাখ্যা

Question: To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg of pure milk is -

Solution:
Let the quantity of water mixed be x kg.
Let CP of 1 kg of pure milk = Tk 1

Hence,
% gain = x × (100/50)
⇒ 10 = 100x/50
⇒ 100x = 500
⇒ x = 5

৪৫৭.

The ratio of syrup and water in a mixture is 3 : 1, the percentage of water in this mixture is -

ক
ক) 75%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 80%

সঠিক উত্তর: গ

গ) 25%

উত্তর

সঠিক উত্তর: গ

গ) 25%

গ

ব্যাখ্যা

Question: The ratio of syrup and water in a mixture is 3 : 1, the percentage of water in this mixture is -

Solution:
Percentage of water = (1/4) × 100% = 25%

৪৫৮.

A man bought some sugar and salt for Tk. 440. The ratio of the weights of sugar and salt is 5 : 2, and the price per unit weight of sugar and salt is in the ratio 6 : 7. What is the price of the total sugar?

ক
Tk. 280
খ
Tk. 300
গ
Tk. 320
ঘ
Tk. 340

সঠিক উত্তর: খ

Tk. 300

উত্তর

সঠিক উত্তর: খ

Tk. 300

খ

ব্যাখ্যা

Question: A man bought some sugar and salt for Tk. 440. The ratio of the weights of sugar and salt is 5 : 2, and the price per unit weight of sugar and salt is in the ratio 6 : 7. What is the price of the total sugar?

Solution:
Given,
Weight ratio (Sugar : Salt) = 5 : 2
Price ratio per unit weight (Sugar : Salt) = 6 : 7

Total price ratio of sugar and salt = (Weight × Price per unit)
= 5 × 6 : 2 × 7
= 30 : 14
= 15 : 7

Total units = 15 + 7 = 22 units

Accordint to the question,
22 units = Tk. 440
⇒ 1 unit = 440/22
∴ 1 unit= Tk. 20

∴ Price of total sugar = 15 × 20 = Tk. 300

৪৫৯.

A merchant has 100 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is-

ক
60 kg
খ
50 kg
গ
75 kg
ঘ
80 kg

সঠিক উত্তর: ক

60 kg

উত্তর

সঠিক উত্তর: ক

60 kg

ক

ব্যাখ্যা

Question: A merchant has 100 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is-

Solution:
By the rule of alligation, we have:

⇒ Quantity of cheaper : Quantity of Dearer = (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper)
⇒ Quantity of cheaper : Quantity of Dearer = (18-14) : (14-8)
= 4 : 6
= 2 : 3

∴ Quantity of 2nd kind = (3/5 × 100) kg
= 60 kg

৪৬০.

Find the ratio of purchase price to sell price if there is loss of 12.5%?

ক
ক) 7 : 8
খ
খ) 8 : 7
গ
গ) 2 : 25
ঘ
ঘ) 25 : 2

সঠিক উত্তর: খ

খ) 8 : 7

উত্তর

সঠিক উত্তর: খ

খ) 8 : 7

খ

ব্যাখ্যা

ধরি, ক্রয়মূল্য 100 টাকা
12.5% ক্ষতিতে বিক্রয়মূল্য (100 - 12.5) = 87.5 টাকা
ক্রয়মূল্য : বিক্রয়মূল্য = 100 : 87.5 = 8 : 7

৪৬১.

Tk. 700 is received among A,B and C so that A receives half as much as B and B half as much as C. Then C’s share is:

ক
ক) 200
খ
খ) 300
গ
গ) 400
ঘ
ঘ) 500
ঙ
ঙ) 600

সঠিক উত্তর: গ

গ) 400

উত্তর

সঠিক উত্তর: গ

গ) 400

গ

ব্যাখ্যা

Let C = x
Then B = x/2
and A = x/4
A : B : C = 1 : 2 : 4
C's share = Tk. (4/7 × 700) = 400

৪৬২.

Milk and water are in the ratio of 4 : 5 in a mixture of 45 liters. To make the ratio equal how much milk should be added to the mixture ?

ক
5 liters
খ
9 liters
গ
10 liters
ঘ
15 liters

সঠিক উত্তর: ক

5 liters

উত্তর

সঠিক উত্তর: ক

5 liters

ক

ব্যাখ্যা

Question: Milk and water are in the ratio of 4 : 5 in a mixture of 45 liters. To make the ratio equal how much milk should be added to the mixture ?

Solution:
amount of milk
= (4/9)×45
= 20 litres
amount of water
= (5/9)×45
= 25 litres

the amount of milk to be added is
= (25-20)
= 5 litres.

৪৬৩.

An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of copper and lead per kg in new alloy will be-

ক
1/4 and 1/6
খ
1/6 and 1/8
গ
1/8 and 1/4
ঘ
11/24 and 1/6
ঙ
11/24 and 1/8

সঠিক উত্তর: ঙ

11/24 and 1/8

উত্তর

সঠিক উত্তর: ঙ

11/24 and 1/8

ঙ

ব্যাখ্যা

Question: An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of copper and lead per kg in new alloy will be-

Solution:
Ratio of Zinc, Copper and Tin is given as, Z : C : T = 2 : 3 : 1 = 4 : 6 : 2
Now, let the first alloy be 12 kg (taken as 4 kg Zinc, 6 kg Copper and 2 Kg Tin)
Weight of second alloy = 12 kg as, C : T : L = 5 : 4 : 3 (taken as 5 kg Copper, 4 kg Tin and 3 Kg Lead)

Alloys are mixed together to form third alloy. Then the ratio of content in it,
Z : C : T : L = 4 : (6 + 5) : (2 + 4) : 3 = 4 : 11 : 6 : 3

Weight of third alloy = 12 + 12 = 24 Kg.
∴ Weight of Copper = 11/24
And, weight of Lead = 3/24
= 1/8

৪৬৪.

A milkman claims to sell milk at its cost price, still, he is making a profit of 30% since he has mixed some amount of water in the milk. What is the % of milk in the mixture?

ক
ক) 71.02%
খ
খ) 76.92%
গ
গ) 63.22%
ঘ
ঘ) 86.42%

সঠিক উত্তর: খ

খ) 76.92%

উত্তর

সঠিক উত্তর: খ

খ) 76.92%

খ

ব্যাখ্যা

Let the milk he bought is 1000 ml
Let C.P of 1000 ml is Tk. 100

Here let he is mixing K ml of water
He is getting 30% profit

⇒ Now, the selling price is also Tk. 100 for 1000 ml
⇒ 100 : K%
⇒ 100 : 30
10 : 3 is the ratio of milk to water

Percentage of milk = 10 x 100/13
= 1000/13
= 76.92%

৪৬৫.

If 8 men and 3 boys working together can do five times as much work per hour as a man and a boy together, working capacities of a man and a boy are in the ratio-

ক
3 : 2
খ
2 : 3
গ
3 : 4
ঘ
4 : 3

সঠিক উত্তর: খ

2 : 3

উত্তর

সঠিক উত্তর: খ

2 : 3

খ

ব্যাখ্যা

Question: If 8 men and 3 boys working together can do five times as much work per hour as a man and a boy together, working capacities of a man and a boy are in the ratio-

Solution:
Let,
1 man 1 day work = p
1 boy 1 day work = q

Now,
8p + 3q = 5(p + q)
or, 8p + 3q = 5p + 5q
or, 8p - 5p = 5q - 3q
or, 3p = 2q
or, p/q = 2/3
∴ p : q = 2 : 3

৪৬৬.

In a 50-liter mixture of milk and water, the ratio of milk to water is 4 : 1. How much more water must be added to change the ratio to 2 : 3?

ক
45 liters
খ
50 liters
গ
60 liters
ঘ
40 liters

সঠিক উত্তর: খ

50 liters

উত্তর

সঠিক উত্তর: খ

50 liters

খ

ব্যাখ্যা

Question: In a 50-liter mixture of milk and water, the ratio of milk to water is 4 : 1. How much more water must be added to change the ratio to 2 : 3?

Solution:
Given that,
Milk : Water = 4 : 1
Total mixture = 50 liters

Milk = (50 of 4/5) = 40 liters
Water = (50 of 1/5) = 10 liters
Let x = additional water to be added.
New water = 10 + x liters

ATQ,
⇒ 40 : 10 + x = 2 : 3
⇒ 40/(10 + x) = 2/3
⇒ 20 + 2x = 120
⇒ 2x = 120 - 20
⇒ 2x = 100
⇒ x = 100/2
∴ x = 50
∴ 50 liters of water must be added to achieve the 2 : 3 ratio.

৪৬৭.

How much water should be added to 80 liters of pure milk to gain extra 20% profit when selling the mixture at the price of pure milk?

ক
6 liters
খ
12 liters
গ
8 liters
ঘ
16 liters

সঠিক উত্তর: ঘ

16 liters

উত্তর

সঠিক উত্তর: ঘ

16 liters

ঘ

ব্যাখ্যা

Question: How much water should be added to 80 liters of pure milk to gain extra 20% profit when selling the mixture at the price of pure milk?

Solution:
Let’s assume,
Price of pure milk per liter = 100 Taka
So, the price of 50 liters of pure milk = 100 × 80 = 8000 Taka

Now assume,
Water added to the milk = x liters
Then the total quantity of the milk-water mixture = (80 + x) liters

Since the mixture is sold at the price of pure milk,
The selling price of (80 + x) liters = 100(80 + x) Taka

According to the question,
100(80 + x) = 8000 + 8000 of 20%
⇒ 8000 + 100x = 8000 + {8000 × (20/100)}
⇒ 8000 + 100x = 8000 + 1600
⇒ 8000 - 8000 + 100x = 1600
⇒ 100x = 1600
⇒ x = 1600/100
⇒ x = 16

∴ Amount of water to be added = 16 liters

৪৬৮.

The present age of Jamal and Kamal are in the ratio of 6 : 4. Five years ago, their ages were in the ratio of 5 : 3. How old is Jamal now?

ক
ক) 30 years
খ
খ) 35 years
গ
গ) 40 years
ঘ
ঘ) 45 years

সঠিক উত্তর: ক

ক) 30 years

উত্তর

সঠিক উত্তর: ক

ক) 30 years

ক

ব্যাখ্যা

Let, the present ages of Jamal and Kamal are 6x and 4x respectively.
(6x - 5)/(4x - 5) = 5/3
20x - 25 = 18x - 15
2x = 10
x = 5

Habib's age = 6 × 5 = 30 years

৪৬৯.

A jar contains milk and water in the ratio 5 : 1. If the quantity of milk is more than that of water by 8 liters, then what is the quantity of water?

ক
ক) 1.5 liter
খ
খ) 2 liter
গ
গ) 6 liter
ঘ
ঘ) 8 liter

সঠিক উত্তর: খ

খ) 2 liter

উত্তর

সঠিক উত্তর: খ

খ) 2 liter

খ

ব্যাখ্যা

ধরি,
দুধ আছে = 5x লিটার এবং পানি আছে = x লিটার

শর্তমতে,
5x - x = 8
⇒ 4x = 8
⇒ x = 8/4
x = 2

পানি আছে = 2 লিটার

৪৭০.

The cost of Type 1 rice is Tk. 15 per kg and Type 2 rice is Tk. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is-

ক
Tk. 19.50
খ
Tk. 19
গ
Tk. 18
ঘ
Tk. 18.50

সঠিক উত্তর: গ

Tk. 18

উত্তর

সঠিক উত্তর: গ

Tk. 18

গ

ব্যাখ্যা

Question: The cost of Type 1 rice is Tk. 15 per kg and Type 2 rice is Tk. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is-

Solution:
Let the price of the mixed variety be Rs. x per kg.
By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice

∴(20 - x)/(x - 15) = 2/3
⇒ 60 - 3x = 2x - 30
⇒ x = 18.

৪৭১.

A purse contains 342 coins consisting of one Taka, 50 cents and 25 cents coins. If their values are in the ratio of 11 : 9 : 5 then find the number of 50 cents coins?

ক
180
খ
150
গ
162
ঘ
99

সঠিক উত্তর: গ

162

উত্তর

সঠিক উত্তর: গ

162

গ

ব্যাখ্যা

Let the value of one taka, 50 cents, and 25 cents be 11x, 9x, 5x respectively.

No. of 1 taka coins = (11x / 1) =11x
No. of 50 cents coins = (9x / 0.5) = 18x
No. of 25 cents coins = (5x / 0.25) = 20x

11x + 18x + 9x = 342
⇒ 38x = 342
⇒ x = 9

Therefore, no. of 1 taka coins = 11 x 9 = 99 coins
No. of 50 cents coins = 18 x 9 = 162 coins
No. of 25 cents coins = 20 x 9 = 180 coins.

৪৭২.

Abid, Bulbul, and Kabil are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Abir withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Kabil's is-

ক
1250 Tk
খ
1160 Tk
গ
1270 Tk
ঘ
1320 Tk
ঙ
None of the above

সঠিক উত্তর: ঙ

None of the above

উত্তর

সঠিক উত্তর: ঙ

None of the above

ঙ

ব্যাখ্যা

Question: Abid, Bulbul, and Kabil are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Abir withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Kabil's is -

Solution:
Ratio of initial investments = 1/3 : 1/4 : 1/5
= 20 : 15 : 12

Let their initial investments be 20x, 15x and 12x respectively.

Abid : Bulbul : Kabil = (20x × 15) + (10x × 15): (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

Sum of the ratio = 5 + 5 + 4 = 14.
∴ Kabil's share = 4340 × (4/14)
= 1240 Tk.

৪৭৩.

If the diameter of a circle is 4π, then what is the ratio between radius and Circumference of circle-

ক
2 : 3π
খ
2 : 5π
গ
1 : 2π
ঘ
2π : 3

সঠিক উত্তর: গ

1 : 2π

উত্তর

সঠিক উত্তর: গ

1 : 2π

গ

ব্যাখ্যা

Question: If the diameter of a circle is 4π, then what is the ratio between radius and Circumference of circle-

Solution:
Here
The diameter of the circle is d = 4π
So the radius of the circle r = 2π

∴ Circumference of circle = 2. π. 2π
= 4π²

So the ratio between radius and Circumference of circle = 2π : 4π²
=2π/4π²
= 1 : 2π

৪৭৪.

A container filled liquid containing 4 parts of water and 6 parts of milk. How much of the mixture must be drawn off and filled with water so that the mixture contains half and half water?

ক
ক) 1/3
খ
খ) 1/6
গ
গ) 1/4
ঘ
ঘ) 1/5

সঠিক উত্তর: খ

খ) 1/6

উত্তর

সঠিক উত্তর: খ

খ) 1/6

খ

ব্যাখ্যা

Question: A container filled liquid containing 4 parts of water and 6 parts of milk. How much of the mixture must be drawn off and filled with water so that the mixture contains half and half water?

Solution:
Let water = 40 liters
and milk is 60 liters.

Let, x amount taken out from the mixture.
Water = 40 - x × (2/5) + x
and milk = 60 - x × (3/5)

ATQ,

Equate both the equation, we get x = 50/3
Now, mixture drawn ff = (50/3) / 100 = 1/6

৪৭৫.

5 years ago the ratio of father's age to son's age was 5:1 and 2 years later father's age will be 3 times his son's age. What is the ratio of their present age?

ক
ক) 5:6
খ
খ) 7:3
গ
গ) 10:3
ঘ
ঘ) 11:7

সঠিক উত্তর: গ

গ) 10:3

উত্তর

সঠিক উত্তর: গ

গ) 10:3

গ

ব্যাখ্যা

মনেকরি,
5 বছর পূর্বে পিতার বয়স = 5x বছর
এবং পুত্রের বয়স =x বছর
∴ বর্তমানে পিতার বয়স = (5x+5) বছর
এবং পুত্রের বয়স = (x + 5) বছর
প্রশ্নমতে, 5x + 5 + 2 = 3 (x + 5 + 2)
⇒ 5x + 7 = 3(x + 7)
⇒ 5x + 7 = 3x + 21
⇒ 2x = 14
⇒ x=7
∴ বর্তমানে পিতার বয়স 5×7+5 = 40 বছর
বর্তমানে পুত্রের বয়স = 7 + 5 = 12 বছর
∴ পিতা ও পুত্র = 40 : 12 =10 : 3

৪৭৬.

If two times X is equal to three times of Y and also equal to four times of Z, then X : Y : Z is -

ক
4 : 6 : 3
খ
2 : 3 : 4
গ
6 : 4 : 3
ঘ
3 : 4 : 2

সঠিক উত্তর: গ

6 : 4 : 3

উত্তর

সঠিক উত্তর: গ

6 : 4 : 3

গ

ব্যাখ্যা

Question: If two times X is equal to three times of Y and also equal to four times of Z, then X : Y : Z is -

Solution:
2X = 3Y
Or, Y = 2X/3
and 2X = 4Z
Or, Z = X/2

Hence, X : Y : Z = X : 2X/3 : X/2
= 1 : 2/3 : 1/2
= 6 : 4 : 3

৪৭৭.

একটি পার্টিতে মহিলা ও পুরুষের অনুপাত ৩ : ২। যদি আরও ২০ জন পুরুষ পার্টিতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। পার্টিতে কতজন মহিলা ছিল?

ক
২০ জন
খ
১৮ জন
গ
২৪ জন
ঘ
২২ জন
ঙ
কোনটিই নয়

সঠিক উত্তর: গ

২৪ জন

উত্তর

সঠিক উত্তর: গ

২৪ জন

গ

ব্যাখ্যা

প্রশ্ন: একটি পার্টিতে মহিলা ও পুরুষের অনুপাত ৩ : ২। যদি আরও ২০ জন পুরুষ পার্টিতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। পার্টিতে কতজন মহিলা ছিল?

সমাধান:
ধরি,
পার্টিতে মহিলা ও পুরুষের সংখ্যা যথাক্রমে ৩ক এবং ২ক।

প্রশ্নমতে,
৩ক/(২ক + ২০) = ২/৩
⇒ ৯ক = ৪ক + ৪০
⇒ ৫ক = ৪০
∴ ক = ৮

অতএব, মহিলার সংখ্যা ছিল = (৩ × ৮) = ২৪ জন

৪৭৮.

One-third of Anas' investment in National Savings Certificate is equal to one-half of his investment in FDR. If he has Tk. 150000 as total investment. how much he invested in FDR?

ক
Tk. 90000
খ
Tk. 60000
গ
Tk. 75000
ঘ
Tk. 30000

সঠিক উত্তর: খ

Tk. 60000

উত্তর

সঠিক উত্তর: খ

Tk. 60000

খ

ব্যাখ্যা

Question: One-third of Anas' investment in National Savings Certificate is equal to one-half of his investment in FDR. If he has Tk. 150000 as total investment. how much he invested in FDR?

Solution:
Let,
Investment in National Savings Certificate be Tk. x
Investment in FDR be Tk.(150000 - x)

ATQ,
x/3 = (1/2)(150000 - x)
⇒ x/3 = 75000 - x/2
⇒ (x/3) + (x/2) = 75000
⇒ (2x + 3x)/6= 75000
⇒ 5x/6 = 75000
⇒ x = (75000 × 6)/5
∴ x = 90000

∴ Investment in FDR is Tk.(150000 - 90000) = Tk. 60000

৪৭৯.

In a certain zoo, the ratio of tigers to lions to snakes in stock is 3 : 5 : 7. If there are 48 lions and snakes total in stock, how many tigers are there?

ক
10
খ
12
গ
18
ঘ
30

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In a certain zoo, the ratio of tigers to lions to snakes in stock is 3 : 5 : 7. If there are 48 lions and snakes total in stock, how many tigers are there?

Solution:
5x + 7x = 48
⇒ 12x = 48
⇒ x = 48/12 = 4

number of tigers = 3x
= 3 × 4
= 12

৪৮০.

150 liters of a mixture contains 20% water. What amount of additional water should be added such that the water content be raised to 25%?

ক
10 liters
খ
8 liters
গ
12 liters
ঘ
6 liters

সঠিক উত্তর: ক

10 liters

উত্তর

সঠিক উত্তর: ক

10 liters

ক

ব্যাখ্যা

Question: 150 liters of a mixture contains 20% water. What amount of additional water should be added such that the water content be raised to 25%?

Solution:
water in the mixture = 20% of 150 = 30 liters

Let, x liters of water were added to the mixture to make water 25% of the new mixture.

ATQ,
30 + x = 25% of (150 + x)
⇒ 30 + x = (1/4) × (150 + x)
⇒ 120 + 4x = 150 + x
⇒ 3x = 30
⇒ x = 10

৪৮১.

100kg of solution A is mixed with 60kg of solution B. If solution A has tin and copper in the ratio 1 : 4 and solution B has lead and tin in the ratio 3 : 2, then what is the amount of tin in the new solution?

ক
ক) 70kg
খ
খ) 36kg
গ
গ) 44kg
ঘ
ঘ) 56kg

সঠিক উত্তর: গ

গ) 44kg

উত্তর

সঠিক উত্তর: গ

গ) 44kg

গ

ব্যাখ্যা

Question: 100kg of solution A is mixed with 60kg of solution B. If solution A has tin and copper in the ratio 1 : 4 and solution B has lead and tin in the ratio 3 : 2, then what is the amount of tin in the new solution?

Solution:
A এর মিশ্রণে টিনের পরিমাণ = (100 এর 1/(1 + 4)} কেজি
= 20 কেজি

B এর মিশ্রণে টিনের পরিমাণ =(60 এর 2/(3 + 2)} কেজি
= 24 কেজি

A এবং B এর মিশ্রণে মোট টিনের পরিমাণ = (20 + 24)কেজি
= 44 কেজি

৪৮২.

Anis's and Bulbul's shares in a business are in the ratio of 5 : 3. If Anis has invested Tk. 70000 for 12 months, for what period Bulbul has invested Tk. 60000?

ক
12 months
খ
9.4 months
গ
6 months
ঘ
8.4 months

সঠিক উত্তর: ঘ

8.4 months

উত্তর

সঠিক উত্তর: ঘ

8.4 months

ঘ

ব্যাখ্যা

Question: Anis's and Bulbul's shares in a business are in the ratio of 5 : 3. If Anis has invested Tk. 70000 for 12 months, for what period Bulbul has invested Tk. 60000?

Solution:
Let,
Bulbul has invested for x months
Anis : Bulbul = (70000 × 12) : (60000 × x) = 5 : 3
⇒ 84 : 6x = 5 : 3
⇒ 14 : x = 5 : 3
⇒ 14/x = 5/3
⇒ 5x = 42
⇒ x = 42/5
∴ x = 8.4

৪৮৩.

A 180 liter mixture of milk and water contains 20% water. How much milk, in liters must be added to the mixture will contain water and milk in the ratio of 1 : 7

ক
100 liter
খ
108 liter
গ
144 liter
ঘ
252 liter

সঠিক উত্তর: খ

108 liter

উত্তর

সঠিক উত্তর: খ

108 liter

খ

ব্যাখ্যা

Question: A 180 liter mixture of milk and water contains 20% water. How much milk, in liters must be added to the mixture will contain water and milk in the ratio of 1 : 7?

Solution:
Water in the mixtue = 180 × (20/100) liter
= 36 liter

Milk in the mixture = 180 - 36 liter
= 144

Let,
X liter milk must be added

ATQ,
36/(144 + X) = 1/7
⇒ 144 + X = 252
⇒ X = 252 - 144
∴ X = 108 liter

৪৮৪.

The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

ক
15 : 16
খ
17 : 18
গ
11 : 12
ঘ
19 : 20

সঠিক উত্তর: খ

17 : 18

উত্তর

সঠিক উত্তর: খ

17 : 18

খ

ব্যাখ্যা

Question: The ratio of the ages of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

Solution:
Ratio of ages of Boys A and B
Present age 5x : 6x
∴ After two years their ages are (5x + 2) and (6x + 2).

According to the question,
(5x + 2) : (6x + 2) = 7 : 8
⇒ 40x + 16 = 42x + 14
⇒ 2x = 2
∴ x = 1

∴ Present age A = 5 × 1 = 5
∴ Present age B = 6 × 1 = 6
After 12 years A = 5 + 12 = 17
After 12 years B = 6 + 12 = 18
∴ A/B = 17/18

৪৮৫.

Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is-

ক
10 : 9
খ
6 : 5
গ
7 : 8
ঘ
9 : 10

সঠিক উত্তর: গ

7 : 8

উত্তর

সঠিক উত্তর: গ

7 : 8

গ

ব্যাখ্যা

Question: Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is-

Solution:
Given that,
Two numbers are 30% and 20% less than a third number respectively.

Let the third number be 100.

Now,
First number = 100 - 30% of 100
= 100 - 30
∴ First number = 70
And
Second number = 100 - 20% of 100
= 100 - 20
∴ Second number = 80

∴ Ratio of the first two numbers = First number/Second number
= 70/80
= 7/8

∴ The ratio of the first two numbers is 7 : 8.

৪৮৬.

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?

ক
Tk. 500
খ
Tk. 1500
গ
Tk. 2000
ঘ
Tk. 2200
ঙ
None of these

সঠিক উত্তর: গ

Tk. 2000

উত্তর

সঠিক উত্তর: গ

Tk. 2000

গ

ব্যাখ্যা

Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Tk. 1000 more than D, what is B's share?

Solution:
Let the shares of A, B, C and D be Tk. 5x, Tk. 2x, Tk. 4x and Tk. 3x respectively.
Then,
4x - 3x = 1000
∴ x = 1000.

B's share = Tk. 2x = Tk. (2 × 1000) = Tk. 2000.

৪৮৭.

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

ক
6:10:5
খ
3:5:2
গ
5:8:10
ঘ
3:4:7
ঙ
8:9:6

সঠিক উত্তর: ক

6:10:5

উত্তর

সঠিক উত্তর: ক

6:10:5

ক

ব্যাখ্যা

Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x × 12) : (5x × 12) : (5x × 6)
= 36 : 60 : 30
= 6 : 10 : 5.

৪৮৮.

In what ratio must tea at Tk 62 per kg be mixed with at Tk 72 per kg so that the mixture must be worth Tk 64.5 per kg?

ক
ক) 2 : 1
খ
খ) 3 : 1
গ
গ) 3 : 2
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) 3 : 1

উত্তর

সঠিক উত্তর: খ

খ) 3 : 1

খ

ব্যাখ্যা

Question: In what ratio must tea at Tk 62 per kg be mixed with at Tk 72 per kg so that the mixture must be worth Tk 64.5 per kg?

Solution:
Let the quantity of the tea that is Tk 62 per kg be x kg and that of tea that is Tk 72 per kg be y kg.

Hence, the required ratio is x : y

Price of x kg tea = Tk 62x
Price of y kg tea = Tk 72y

If we mix both varieties of tea, the quantity of the mixture will be x + y.

Now, this mixture is Tk 64.50 per kg.
Hence, the total price of the mixture = Tk 64.50(x + y)

So, 62x + 72y = 64.50 (x+y)
⇒ 62x + 72y = 64.5x + 64.5y
⇒ 64.5x - 62x = 72y - 64.5y
⇒ 2.5x = 7.5y
⇒ x/y = 7.5/2.5
⇒ x/y = 3
So, x : y = 3 : 1

Hence, the required ratio is 3:1.

৪৮৯.

A,B and C enter into a partnership investing Tk 35000, Tk 45000 and Tk 55000. Find the their respective shares in annual profit of 40,500

ক
ক) 10500, 13500, 19500
খ
খ) 10500, 13500, 18500
গ
গ) 10500, 13500, 17500
ঘ
ঘ) 10500, 13500, 16500

সঠিক উত্তর: ঘ

ঘ) 10500, 13500, 16500

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10500, 13500, 16500

ঘ

ব্যাখ্যা

A:B:C = 35000:45000:55000 = 7:9:11
A's share = (7/27) ×40500 = Tk 10500
B's share = (9/27) ×40500 = Tk 13500
C's share = (11/27)×40500 = Tk 16500

৪৯০.

A milkman wants to gain 25% on selling the mixture at cost price, then in what ratio must he mix water with milk?

ক
ক) 1 : 4
খ
খ) 1 : 2
গ
গ) 1 : 3
ঘ
ঘ) 2 : 5

সঠিক উত্তর: ক

ক) 1 : 4

উত্তর

সঠিক উত্তর: ক

ক) 1 : 4

ক

ব্যাখ্যা

Question: A milkman wants to gain 25% on selling the mixture at cost price, then in what ratio must he mix water with milk?

Solution:
Let, the milkman has milk of 100 Tk.
after mixing he sold it in = 100 + 25 = 125 Tk.

In 125, milk is of 100 Tk. and water is of 25 Tk.

∴ The ratio of water and milk is 25 : 100 = 1 : 4

৪৯১.

A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is:

ক
8 : 5
খ
9 : 7
গ
9 : 5
ঘ
8 : 7

সঠিক উত্তর: গ

9 : 5

উত্তর

সঠিক উত্তর: গ

9 : 5

গ

ব্যাখ্যা

Question: A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is:

Solution:
খরগোশের 3 লাফ = কুকুরের 1 লাফ
খরগোশের 1 লাফ = কুকুরের 1/3 লাফ
খরগোশের 5 লাফ = কুকুরের 5/3 লাফ

কুকুরের গতিবেগ : খরগোশের গতিবেগ = 3 : 5/3
= 9 : 5

৪৯২.

The ratio of the cost of two articles is 7 : 3 . The first one was sold at a loss of 20% and the second one was sold at a gain of 40% What is the overall percentage of gain/loss?

ক
ক) 2% loss
খ
খ) 2% gain
গ
গ) 4% loss
ঘ
ঘ) 4% gain

সঠিক উত্তর: ক

ক) 2% loss

উত্তর

সঠিক উত্তর: ক

ক) 2% loss

ক

ব্যাখ্যা

দেওয়া আছে,
১ম টির ক্রয়মূল্য : ২য় টির ক্রয়মূল্য = 7 : 3
মনেকরি, ১ম টির ক্রয়মূল্য = 70 টাকা
এবং ২য় টির ক্রয়মূল্য = 30 টাকা
∴ মোট ক্রয়মূল্য = 70 + 30 = 100 টাকা
এখন,
১ম টির বিক্রয়মূল্য = 80/100 × 70 = 56 টাকা
২য় টির বিক্রয়মূল্য = 140/100 × 30 = 42 টাকা
∴ মোট বিক্রয়মূল্য = 56 + 42 = 98 টাকা
∴ ক্ষতি = 100 - 98 = 2 টাকা

৪৯৩.

The ratio between the perimeter and the length of a rectangle is 7 : 2. If the area of the rectangle is 0.12 sq. m, what is the breadth of the rectangle?

ক
30 cm
খ
10 cm
গ
12 cm
ঘ
15 cm
ঙ
18 cm

সঠিক উত্তর: ক

30 cm

উত্তর

সঠিক উত্তর: ক

30 cm

ক

ব্যাখ্যা

2 ( length + breadth ) / length = 7/2
or, ( length + breadth ) / length = 7/4
or, 4 × breadth + 4 × length = 7 × length
∴ length = 4 × breadth / 3

Area = 0.12 square meter = 0.12 × 100 × 100 square centimeter
∴ length × breadth = 1200 square centimeter
or, breadth × 4 × breadth / 3 = 1200
or, breadth ² = 900 = 30² square centimeter
∴ breadth = 30cm

৪৯৪.

The annual incomes and expenditures of a man and his wife are in the ratio of 5 : 3 and 3 : 1 respectively. If they decide to save equally and find a balance of Tk. 4000 at the end of the year, what was the income of the husband?

ক
ক) 2000
খ
খ) 3000
গ
গ) 4000
ঘ
ঘ) 5000
ঙ
ঙ) 6000

সঠিক উত্তর: ঘ

ঘ) 5000

উত্তর

সঠিক উত্তর: ঘ

ঘ) 5000

ঘ

ব্যাখ্যা

Let, annual income of husband and wife respectively = 5x and 3X
Annual expenditure husband and wife respectively = 3y and y
Saving of wife = (3x - y)
Saving of husband = (5x - 3y)
ATQ,
3x - y = 2000
=> y = (3x - 2000)
And,
5x - 3y = 2000
=> 5x - 3(3x - 2000) = 2000
=> 5x - 9x + 6000 = 2000
=> x = 1000
So, Husband's Income = 5 × 1000 = 5000

৪৯৫.

The ratio of milk and water in a pot is 5:2. If the quantity of milk is 6 litre more than quantity of water, then what is the quantity of milk in the pot in litre?

ক
4
খ
16
গ
20
ঘ
10

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The ratio of milk and water in a pot is 5:2. If the quantity of milk is 6 litre more than quantity of water, then what is the quantity of milk in the pot in litre?

Solution:
দেওয়া আছে,
একটি পাত্রে দুধ ও পানির পরিমাণের অনুপাত = 5:2
এবং পাত্রে দুধের পরিমাণ পানির পরিমাণ অপেক্ষা 6 লিটার বেশি।

মনে করি,
পাত্রে দুধের পরিমাণ 5x লিটার
পাত্রে পানির পরিমাণ 2x লিটার

প্রশ্নমতে,
5x - 2x = 6
⇒ 3x = 6
⇒ x = 6/3
∴ x = 2

∴ পাত্রে দুধের পরিমাণ (5 × 2) বা 10 লিটার।

৪৯৬.

Three numbers A, B and C are in the ratio 1 : 2 : 3. Their average is 600. If A is increased by 10% and B is decreased by 20%, then to get the average increased by 5%, C will be increased by-

ক
180 Tk
খ
280 Tk
গ
380 Tk
ঘ
580 Tk

সঠিক উত্তর: ক

180 Tk

উত্তর

সঠিক উত্তর: ক

180 Tk

ক

ব্যাখ্যা

Question: Three numbers A, B and C are in the ratio 1 : 2 : 3. Their average is 600. If A is increased by 10% and B is decreased by 20%, then to get the average increased by 5%, C will be increased by-

Solution:
Let
A= x, B = 2x, C = 3x.
Then,
x + 2x + 3x = 600 × 3
→ 6x = 1800
→ x = 300

So, A =300, B = 600, C = 900.
New value of A = 110% of 300 = 330
New value of B = 80% of 600 = 480
New average = 105% of 600 = 630

∴ New value of C = (630 × 3) - (330 + 480)=1080
→ Increase in value of C = 1080 - 900 = 180 Tk.

৪৯৭.

ক
ক) 9 : 11 : 13
খ
খ) 9 : 8 : 13
গ
গ) 9 : 8 : 10
ঘ
ঘ) 7 : 8 : 12

সঠিক উত্তর: গ

গ) 9 : 8 : 10

উত্তর

সঠিক উত্তর: গ

গ) 9 : 8 : 10

গ

ব্যাখ্যা

2A/3 = 75B/100 = 6C/10
A/B = 9/8
B/C = 8/10
A : B : C = 9 : 8 : 10

৪৯৮.

P and Q started a business investing Tk 85000 and Tk 15000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?

ক
ক) 3 : 4
খ
খ) 17 : 3
গ
গ) 15 : 23
ঘ
ঘ) 3 : 5

সঠিক উত্তর: খ

খ) 17 : 3

উত্তর

সঠিক উত্তর: খ

খ) 17 : 3

খ

ব্যাখ্যা

Question: P and Q started a business investing Tk 85000 and Tk 15000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?

Solution:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.

ATQ,
P : Q = 2 × 85000 : 2 ×15000
= 85 : 15
= 17 : 3

৪৯৯.

The ages of Jamir and Amir are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages?

ক
8 Years
খ
6 Years
গ
4 Years
ঘ
2 Years
ঙ
None

সঠিক উত্তর: ঘ

2 Years

উত্তর

সঠিক উত্তর: ঘ

2 Years

ঘ

ব্যাখ্যা

Question: The ages of Jamir and Amir are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages?

Solution:
Let, Jamir's age be = 8x years,
Then Amir's age = 7x years

According to the question,
∴ (8x + 10)/(7x + 10) = 13/12
⇒ 12(8x + 10) = 13(7x + 10)
⇒ 96x + 120 = 91x + 130
⇒ 5x = 10
⇒ x = 2

Difference between their ages
= (8x - 7x)
= x years
= 2years

৫০০.

A wheel that has 6 cogs has meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, the number of revolutions made by the larger wheel will be-

ক
ক) 4
খ
খ) 9
গ
গ) 12
ঘ
ঘ) 49

সঠিক উত্তর: খ

খ) 9

উত্তর

সঠিক উত্তর: খ

খ) 9

খ

ব্যাখ্যা

Question: A wheel that has 6 cogs has meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, the number of revolutions made by the larger wheel will be-

Solution:
Let the required number of revolutions made by the larger wheel be x.
We know, More cogs ⟹ Less revolutions

So, it is Indirect Proportion.
∴ 14 : 6 : : 21 : x
⇒ 14 × x = 6 × 21
⇒ x = (6 × 21)/14
⇒ x = 9

Hence, the number of revolutions made by the larger wheel is 9