লগ ইননিবন্ধন
বিষয়সমূহ

PrepBank · বিষয়ভিত্তিক প্রশ্ন

Ratio & Proportion, Alligation or Mixture

মোট প্রশ্ন১,০৮৬এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Ratio & Proportion, Alligation or Mixture

PrepBank · পাতা ১০ / ১১ · ৯০১–১,০০০ / ১,০৮৬

৯০১.
700 ml of a mixture contains water and milk in the ratio 2 : 8. How much water must be added to the mixture so that the ratio of water and milk becomes 3 : 8?
  1. ক
    70 ml
  2. খ
    75 ml
  3. গ
    60 ml
  4. ঘ
    65 ml
ব্যাখ্যা
Question: 700 ml of a mixture contains water and milk in the ratio 2 : 8. How much water must be added to the mixture so that the ratio of water and milk becomes 3 : 8?

Solution:
Milk in the 700 ml of mixture = 700 × (8/10)  = 560 ml

So, water in the mixture would be = 700 - 560 = 140 ml

Let water to be added = x ml

Now, 
(140 + x)/560 = 3/8
1120 + 8x = 1680
8x = 1680 - 1120
8x= 560
x = 560/8 = 70 ml
৯০২.
A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog is equal to 4 leaps of the hare. Compare their speeds:
  1. ক
    16 : 15
  2. খ
    18 : 17
  3. গ
    19 : 18
  4. ঘ
    20 : 19
ব্যাখ্যা
Question: A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog is equal to 4 leaps of the hare. Compare their speeds:

Solution: 
খরগোশের 5 লাফ নিতে সময় লাগে t s
কুকুরের 4 লাফ নিতে সময় লাগে t s

খরগোশ 4 লাফে যায় x কিমি 
5 লাফে যাবে 5x/4 কিমি

কুকুর 3 লাফে যায় x কিমি 
4 লাফে যাবে 4x/3 কিমি

বেগের অনুপাত = (4x/3)/t : (5x/4)/t
= (4/3) : (5/4)
= 16 : 15
৯০৩.
A grocer wishes to sell a mixture of two variety of pulses worth Tk.16 per KG. In what ratio must he mix the pulses to reach this selling price, when cost of one variety of pulses is Tk.14 per KG and the other is Tk.24 per KG?
  1. ক
    ক) 4 : 1
  2. খ
    খ) 3 : 4
  3. গ
    গ) 5 : 2
  4. ঘ
    ঘ) 3 : 7
ব্যাখ্যা
প্রশ্ন: A grocer wishes to sell a mixture of two variety of pulses worth Tk.16 per KG. In what ratio must he mix the pulses to reach this selling price, when cost of one variety of pulses is Tk.14 per KG and the other is Tk.24 per KG?

সমাধান:
ধরি,
১৪ টাকার ডাল ছিল ক কিলোগ্রাম
২৪ টাকার ডাল ছিল খ কিলোগ্রাম

শর্তমতে,
১৪ক + ২৪খ = (ক + খ)১৬
বা, ১৪ক + ২৪খ = ১৬ক + ১৬খ
বা, ২৪খ - ১৬খ = ১৬ক - ১৪ক
বা, ৮খ = ২ক
বা, খ/ক = ২/৮
বা, ক/খ = ৮/২
∴ ক : খ = ৮ : ২ = ৪ : ১
৯০৪.
The students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally the total number of students was-
  1. ক
    90
  2. খ
    100
  3. গ
    120
  4. ঘ
    150
ব্যাখ্যা
Question: The students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally the total number of students was-

Solution:
Let the original number of students in three classes be 2x, 3x and 5x respectively.
As given,
(2x + 20)/(3x + 20) = 4/5
⇒ 10x + 100 = 12x + 80
⇒ 12x - 10x = 100 - 80
⇒ 2x = 20
∴ x = 10

Total number of students originally = 2x + 3x + 5x
= 10x
= 10 × 10
= 100
৯০৫.
In what ratio must sugar at Tk 15 per kg be mixed with sugar at Tk 25 per kg so that the mixture is worth Tk 22 per kg?
  1. ক
    1 : 4
  2. খ
    2 : 5
  3. গ
    3 : 7
  4. ঘ
    4 : 9
ব্যাখ্যা
Question: In what ratio must sugar at Tk 15 per kg be mixed with sugar at Tk 25 per kg so that the mixture is worth Tk 22 per kg?

Solution:
Let the amount of sugar at Tk 15 per kg be x kg
and the amount of sugar at Tk 25 per kg be y kg.

ATQ,
15x + 25y = 22(x + y)
⇒ 15x + 25y = 22x + 22y
⇒ 7x = 3y
⇒ x/y = 3/7
⇒ x : y = 3 : 7
৯০৬.
1 year ago the ratio between A's and B' s salary was 3 : 4. Ratios of their individual salaries between last year's and this year's salaries are 4 : 5 & 2 : 3 respectively. At present the total of their salary is TK. 4160. How much is the salary of A now?
  1. ক
    ΤΚ. 1040
  2. খ
    TK. 2560
  3. গ
    TK. 1600
  4. ঘ
    TK. 3120
  5. ঙ
    None of these
ব্যাখ্যা
Question: 1 year ago the ratio between A's and B' s salary was 3 : 4. Ratios of their individual salaries between last year's and this year's salaries are 4 : 5 & 2 : 3 respectively. At present the total of their salary is TK. 4160. How much is the salary of A now?

Solution:
Let,
the salaries of A and B last year be Tk. 3x and Tk. 4x respectively.
Then,
A's present salary = Tk. (5/4) × 3x
= Tk. 15x/4

B's present salary = Tk.(3/2) × 4x
= Tk. 6x.

According to the question,
(15x/4) + 6x = 4160
⇒ 15x + 24x = 4160 × 4
⇒ 39x = 4160 × 4
⇒ x = (4160 × 4)/39

So, A's present salary = Tk. (15/4) × {(4160 × 4)/39}
= Tk.1600
৯০৭.
In a mixture of milk and water, the ratio is 5 : 3. If 4 liters of water is added, the new ratio becomes 5 : 4. What was the original amount of milk in the mixture?
  1. ক
    20 liters
  2. খ
    28 liters
  3. গ
    32 liters
  4. ঘ
    36 liters
ব্যাখ্যা

Question: In a mixture of milk and water, the ratio is 5 : 3. If 4 liters of water is added, the new ratio becomes 5 : 4. What was the original amount of milk in the mixture?

Solution:
ধরি, শুরুতে দুধ ছিল = 5x লিটার,
পানি ছিল = 3x লিটার।

এখন ৪ লিটার পানি যোগ করলে,
নতুন পানি = 3x + 4 লিটার

ATQ,
5x/(3x + 4) = 5/4
⇒ 4 × 5x = 5 × (3x + 4)
⇒ 20x = 15x + 20
⇒ 5x = 20
⇒ x = 4

∴ দুধের পরিমাণ = 5x = 5 × 4 = 20 লিটার

৯০৮.
In what ratio must sugar at Tk 12 per kg be mixed with sugar at Tk. 18 per kg so that the mixture be worth Tk. 15 per kg?
  1. ক
    1 : 1
  2. খ
    2 : 3
  3. গ
    1 : 2
  4. ঘ
    3 : 2 
ব্যাখ্যা

Question: In what ratio must sugar at Tk. 12 per kg be mixed with sugar at Tk. 18 per kg so that the mixture be worth Tk. 15 per kg?

Solution:
Let x kg of sugar at Tk. 12 and y kg of sugar at Tk. 18 be mixed.

ATQ,
⇒ 12x + 18y = 15(x + y)
⇒ 12x + 18y = 15x + 15y
⇒ 15x - 12x = 18y - 15y
⇒ 3x = 3y
∴ x : y = 1 : 1

∴ required ratio 1 : 1.

৯০৯.
Two numbers are in the ratio 3:7. If 6 be added to each of them, then they are in the ratio 5:9. Find the numbers?
  1. ক
    ক) 9 and 21
  2. খ
    খ) 11 and 17
  3. গ
    গ) 7 and 17
  4. ঘ
    ঘ) 13 and 23
ব্যাখ্যা
Let the two numbers be 3x and 7x
⇒ (3x + 6)/(7x + 6) = 5/9
⇒ 27x + 54 = 35x + 30
⇒ 8x = 24
⇒ x = 3
Two numbers are 9 and 21
৯১০.
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
  1. ক
    10/21
  2. খ
    7/16
  3. গ
    1/2
  4. ঘ
    17/35
ব্যাখ্যা

Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

Solution: 
lets, the total cups sold 15 
small cups = (3/5) × 15 = 9 
large cups = 15 - 9 = 6 

let, small cups were sold 6 taka each, then large cups were sold 7 taka each.

large cup's revenue = 7 × 6 = 42 taka 
small cup's revenue = 6 × 9 = 54 taka 

 fraction of Tuesday's total revenue was from the sale of large cups = 42/(42 + 54)
= 42/96 
= 7/16

৯১১.
The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio
  1. ক
    24 : 69 : 94
  2. খ
    25 : 62 : 92
  3. গ
    21 : 67 : 98
  4. ঘ
    21 : 66 : 92
ব্যাখ্যা
Question: The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio

Solution:
Given that
Salary has  in 1 : 3 : 4 ratio
Let
A's Salary = Tk. 100
B's Salary = Tk. 300
C's Salary = Tk. 400

Now,
5% increase in A's Salary,
A's new Salary = (100 + 5% of 100) = Tk. 105

B's Salary increases by 10%, Then,
B's new Salary = (300 + 10% of 300) = Tk. 330

C's Salary increases by 15%,
C's new Salary = (400 + 15% of 400) = Tk. 460

Then, ratio of increased Salary,
A : B : C = 105 : 330 : 460 = 21 : 66 : 92
৯১২.
In a map, 2 cm represents 85 km. The distance between two cities is 9.4 cm on the map. The actual distance between the cities is -
  1. ক
    369. 5 km
  2. খ
    339.5 km
  3. গ
    399.5 km
  4. ঘ
    389.5 km
ব্যাখ্যা

Question: In a map, 2 cm represents 85 km. The distance between two cities is 9.4 cm on the map. The actual distance between the cities is - 

Solution: 
Since 2 cm = 85 km,
Actual Distance = (85/2) × 9.4 
= 799/2
= 399.5 km 

৯১৩.
A mixture contains 2/5 of element A and 3/5 of element B. When 5 ml of A is added to the mixture, the proportion of B in the mixture changes to 1/5. What amount of A was originally present in the mixture before the addition was made?
  1. ক
    1 ml
  2. খ
    1.5 ml
  3. গ
    2.5 ml
  4. ঘ
    6 ml
ব্যাখ্যা
Question: A mixture contains 2/5 of element A and 3/5 of element B. When 5 ml of A is added to the mixture, the proportion of B in the mixture changes to 1/5. What amount of A was originally present in the mixture before the addition was made?

Solution:
Let mixture be x ml.
A = (2x)/5 ml.
B = (3x)/5 ml.

After adding 5 ml of A to mixture, amount of B remained same. 
And the mixure be x + 5 ml.

New B = (x + 5)/5

Now,
(3x)/5 = (x + 5)/5
⇒ 15x = 5x + 25
⇒ 10x = 25
∴ x = 2.5

Original amount of A = (2 × 2.5)/5 ml = 1 ml.
৯১৪.
The ratio, in which tea costs Tk. 192 per kg is to be mixed with tea costing Tk. 150 per kg so that the mixed tea when sold for Tk. 194.40 per kg, gives a profit of 20%
  1. ক
    2 : 5
  2. খ
    3 : 5
  3. গ
    5 : 3
  4. ঘ
    5 : 2
ব্যাখ্যা

CP of first tea = Tk. 192 per kg.
CP of Second tea = Tk. 150 per kg.
The mixture is to be sold in Tk. 194.40 per kg, which has included 20% profit. So,
SP of Mixture = Tk. 194.40 per kg.

Let the CP of Mixture be Tk. X per kg. Therefore,
X + 20% of X = SP
6x/5 = 194.40
6X = 194.40 × 5
X = Tk. 162 per kg.

Let N kg of first tea and M kg of second tea be added.

Now, Using Alligation,
We get,
N/M = 12/30
N/M = 2 : 5

.
৯১৫.
A solution contains 20% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-
  1. ক
    40%
  2. খ
    20.36%
  3. গ
    40.36%
  4. ঘ
    33.33%
ব্যাখ্যা
Question: A solution contains 20% sugar by weight is made sweeter by doubling the amount of sugar. The percent of sugar, by weight, in the new solution is-

Solution: 
let, solution is 100 unit
amount of sugar = 100 × 20%
= 100 × (20/100)
= 20 unit 

by doubling, amount of sweet = 40 unit

solution now = 100 + 20 = 120 unit 

percent of sugar = (40 × 100)/120 %
= 33.33%

 
৯১৬.
If x : 7.5 = 7 : 17.5, then the value of x is-
  1. ক
    ক) 1
  2. খ
    খ) 2.5
  3. গ
    গ) 3
  4. ঘ
    ঘ) 3.5
  5. ঙ
    ঙ) 4
ব্যাখ্যা

x:7.5 = 7:17.5
⇒ 17.5x = 7.5×7
⇒ x = (7.5×7)/17.5
= 3

৯১৭.
An employer pays 3 workers X, Y and Z a total of TK. 36600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?
  1. ক
    9000
  2. খ
    10800
  3. গ
    11700
  4. ঘ
    12000
ব্যাখ্যা
Question: An employer pays 3 workers X, Y and Z a total of TK. 36600 a week. X is paid 125% of the amount Y is paid and 80% of the amount Z is paid. How much does X make a week?

Solution:
X = 125% of Y
⇒ X = 125Y/100
⇒ X/Y = 125/100
∴ X : Y = 5 : 4 = 5 × 4 : 4 × 4 = 20 : 16

X = 80% of Z
⇒ X = 80Z/100
⇒ X/Z = 80/100
∴ X : Z = 4 : 5 = 4 × 5 : 5 × 5 = 20 : 25

∴ X : Y : Z = 20 : 16 : 25

X makes the week = (20/61) × 36600
= 12000
৯১৮.
The ratio of water and alcohol in two different containers is 2 : 3 and 4 : 5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7 : 5?
  1. ক
    ক) 7:3
  2. খ
    খ) 5:3
  3. গ
    গ) 8:5
  4. ঘ
    ঘ) 2:7
  5. ঙ
    ঙ) 3:5
ব্যাখ্যা

W1 : A1 W2 : A2 …… WN : AN
2 : 3 4 : 5 …… 5 : 7
W1/(W1+A1) = 2/5 ; W2/(W2+A2) = 4/9; WN/(WN+AN) = 5/12
= 72/180
= 80/180
= 75/180



=> 5 : 3
Therefore, the ratio is 5 : 3

৯১৯.
A bag contains Tk. 410 in the form of Tk. 5, Tk. 2, and Tk. 1 coins. The number of coins is in the ratio 4: 6: 9. So, find the number of 2 Taka’s coins -
  1. ক
    40
  2. খ
    50
  3. গ
    60
  4. ঘ
    70
ব্যাখ্যা

ATQ,
if the ratio of coins = 4: 6: 9
That means if Tk. 5 coins are 4, Tk. 2 coins are 6, and then Tk. 1 coins are 9.

According to the given ratio, the ratio of amounts = 5 × 4 : 6 × 2: 9 × 1 = 20 : 12 : 9
The sum of the ratios of the amounts = 20 + 12 + 9
= Tk. 41

But ATQ,
it is Tk. 410, which means multiply each ratio by 10
i.e., new ratio = 40 : 60 : 90
Now, 40 × 5 : 60 × 2 : 90 × 1 = 200 : 120 : 90

The total amount in the form of two rupees coins = 120
So, the two rupees coins = 120/2
= 60.

৯২০.
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
  1. ক
    ক) 100
  2. খ
    খ) 150
  3. গ
    গ) 250
  4. ঘ
    ঘ) 260
  5. ঙ
    ঙ) 416
ব্যাখ্যা

Let the number of boys and girls be 8x and 5x.
Total number of students = 13x
= 13 × 32
= 416.

৯২১.
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
  1. ক
    26.34 litres
  2. খ
    27.36 litres
  3. গ
    28 litres
  4. ঘ
    29.16 litres
ব্যাখ্যা
Question: A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

Solution:
Amount of milk left after 3 operations = 40(1 - 4/40)3 litres
= 40 × 36/40 × 36/40 × 36/40
= 40 × 9/10 × 9/10 × 9/10
= 29.16 litres
৯২২.
What number has to be added to the terms of 3 : 5 to make the ratio 5 : 6?
  1. ক
    ক) 5
  2. খ
    খ) 6
  3. গ
    গ) 7
  4. ঘ
    ঘ) 8
ব্যাখ্যা
Question: What number has to be added to the terms of 3 : 5 to make the ratio 5 : 6?

Solution: 
Let the number to be added is X.
Then,
(3 + X)/(5 + X) = 5/6
6(3 + X) = 5(5 + X)
18 + 6X = 25 + 5X
X = 7
৯২৩.
A dishonest milkman profess 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-
  1. ক
    ক) 20%
  2. খ
    খ) 25%
  3. গ
    গ) 15%
  4. ঘ
    ঘ) 10%
ব্যাখ্যা
Question: A dishonest milkman profess 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, the cost price of 1 liter of milk be = 100 Tk
So, the selling price of 1 liter mixture is also = 100 Tk

Here, in 100 Tk, SP gain = 25%
So, cost price of the mixture = (100 × 100)/125 = 80 Tk

So, water in the mixture = 100 - 80 = Tk 20
৯২৪.
When three-fifths of a number are subtracted from two-thirds of the number, the result is 18. What's the number?
  1. ক
    260
  2. খ
    250
  3. গ
    280
  4. ঘ
    270
ব্যাখ্যা
Question: When three-fifths of a number are subtracted from two-thirds of the number, the result is 18. What's the number?

Solution:
Let,
The number be n

ATQ,
(2/3) × n - (3/5) × n = 18
⇒ (2n/3) - (3n/5) = 18
⇒ (10n - 9n)/15 = 18
⇒ n/15 = 18
∴ n = 270
৯২৫.
In a business A and C invested amounts in the ratio 2 : 1 whereas A and B invested amounts in the ratio 3 : 2 . If their annual profit be Tk. 157300, then B's share in the profit is -
  1. ক
    ক) Tk. 24200
  2. খ
    খ) Tk. 24200
  3. গ
    গ) Tk. 48000
  4. ঘ
    ঘ) Tk. 48400
ব্যাখ্যা

A:B = 3:2 = 6:4
A:C = 2:1 = 6:3
A:B:C = 6:4:3
∴ B's share = 4/13 × 157300 = 48400

৯২৬.
A mixture contains two liquids A and B are in the ratio 2 : 1. If 6 litres of mixture is withdrawn and replaced with 6 litres of B, then the ratio becomes 3 : 2. What was the initial quantity of A?
  1. ক
    30 litres
  2. খ
    40 litres
  3. গ
    50 litres
  4. ঘ
    60 litres
ব্যাখ্যা

Question: A mixture contains two liquids A and B are in the ratio 2 : 1. If 6 litres of mixture is withdrawn and replaced with 6 litres of B, then the ratio becomes 3 : 2. What was the initial quantity of A?

Solution:
মনে করি,
মিশ্রণের প্রাথমিক পরিমাণ = 3X লিটার

A এর পরিমাণ = 2X লিটার
B এর পরিমাণ = X লিটার

∴ 6 লিটার মিশ্রণ তুলে নেওয়ার পর,
A এর পরিমাণ = 2X - (2/3) × 6 = (2X - 4) লিটার
B এর পরিমাণ = X - (1/3) × 6 = (X - 2) লিটার

আবার,
B তে 6 লিটার যোগ করার পর,
B এর পরিমাণ = X - 2 + 6 = (X + 4) লিটার

প্রদত্ত অনুপাত,
(2X - 4) /(X + 4) = 3/2
বা, 4X - 8 = 3X + 12
বা, X = 12 + 8
∴ X = 20

তাহলে, A এর পরিমাণ = 2 × 20 = 40 লিটার

৯২৭.
Two numbers are in the ratio 2 : 3. If 4 is subtracted from the first number, the ratio becomes 1 : 2. What are the numbers?
  1. ক
    14, 21
  2. খ
    16, 24
  3. গ
    18, 27
  4. ঘ
    20, 30
ব্যাখ্যা

Question: Two numbers are in the ratio 2 : 3. If 4 is subtracted from the first number, the ratio becomes 1 : 2. What are the numbers?

Solution:
Let the two numbers be: 2x and 3x

According to the question,
(2x - 4)/3x = 1/2
⇒ 2(2x - 4) = 3x
⇒ 4x - 8 = 3x
⇒ x = 8

∴ First number = 2 × 8 = 16
∴ Second number = 3 × 8 = 24

৯২৮.
100 liter solution contains 30% salt. How much water should be evaporated to make the solution 40% salt?
  1. ক
    20 liter
  2. খ
    25 liter
  3. গ
    40 liter
  4. ঘ
    30 liter
  5. ঙ
    None of these
ব্যাখ্যা
Question: 100 liter solution contains 30% salt. How much water should be evaporated to make the solution 40% salt?

Solution:
100 লিটারের 30% লবণ রয়েছে, অর্থাৎ,
(30/100) × 100 = 30 লিটার লবণ

∴ পানির পরিমাণ = 100 - 30 = 70 লিটার

ধরি,
x লিটার পানি বাষ্পীভূত করতে হবে ।
তাহলে নতুন দ্রবণের পরিমাণ হবে, 100 - x লিটার

প্রশ্নমতে,
⇒ 30/(100 - x) = 40/100
⇒ 40(100 - x) = 30 × 100
⇒ 4000 - 40x = 3000
⇒ 40x = 4000 - 3000
⇒ 40x = 1000
⇒ x = 1000/40
⇒ x = 25

∴ 25 লিটার পানি বাষ্পীভূত করতে হবে যাতে লবণের পরিমাণ ৪০% হয়।
৯২৯.
In Live MCQ's class there are 12 boys and 18 girls. Write the ratio of girls : boys in its simplest form.
  1. ক
    12 : 30
  2. খ
    3 : 2
  3. গ
    2 : 3
  4. ঘ
    18 : 12
ব্যাখ্যা
Question: In Live MCQ's class there are 12 boys and 18 girls. Write the ratio of girls : boys in its simplest form.

Solution:
The question asks for the ratio girls:boys so girls must be first and boys second. It also asks for the answer in its simplest form.

Number of girl : Number of boys = 18 : 12 = 3 : 2

The ratio 18 : 12 represents the number of girls to boys but is not in its simplest form. Ratios are typically expressed in the simplest form by dividing both terms by their greatest common divisor.
Here’s the simplification process:
Original Ratio= 18 : 12
Greatest Common Divisor (GCD): The GCD of 18 and 12 is 6.
Simplify: Divide both terms by 6
18/6 : 12/6 = 3 : 2
৯৩০.
Three pots contain 100ml of water, milk, and oil respectively. 10% of the first pot is mixed with the second pot and then 20% of the second pot is mixed with the third pot. How much water is there in the third pot?
  1. ক
    1ml
  2. খ
    3ml
  3. গ
    4ml
  4. ঘ
    2ml
  5. ঙ
    2.5ml
ব্যাখ্যা
Question: Three pots contain 100ml of water, milk, and oil respectively. 10% of the first pot is mixed with the second pot and then 20% of the second pot is mixed with the third pot. How much water is there in the third pot?

Solution: 
After mixing 10% water from the first pot to the second pot,
total mixture = 100 ml + (10% of 100ml) = 110ml
in 110 ml,
water = 10ml,
milk = 100 ml,

20% of the second pot is mixed with the third pot.
20% of the second pot contains = (20% of 110) ml = 22ml mixture.

in a 22ml mixture of the second pot,
water = (10/110)22 ml = 2ml
milk = (100/110)22 ml= 20ml
৯৩১.
The ratio of milk to water in a mixture is 5 : 3. If 6 liters of milk are added to the mixture, the new ratio of milk to water becomes 8 : 3. Find the final amount of milk in the new mixture.
  1. ক
    10 liters
  2. খ
    14 liters
  3. গ
    16 liters
  4. ঘ
    21 liters
ব্যাখ্যা

Question: The ratio of milk to water in a mixture is 5 : 3. If 6 liters of milk are added to the mixture, the new ratio of milk to water becomes 8 : 3. Find the final amount of milk in the new mixture.

Solution:
Let the initial amount of milk be 5x liters
and the amount of water 3x liters.

ATQ,
Ratio of milk and water after adding 6 liters of milk
(5x + 6)/3x = 8/3
⇒ 3(5x + 6) = 8 × 3x
⇒ 15x + 18 = 24x
⇒ 18 = 9x
⇒ x = 2

∴ Final amount of milk in mixture = 5x + 6
= (5 × 2) + 6
= 10 + 6 = 16 liters.

৯৩২.
An alloy of copper and nickel contains 65% copper. A second alloy contains copper and nickel in the ratio 17 : 3. In what ratio should the two alloys be mixed so that the new mixture contains 4 times as much copper as nickel?
  1. ক
    4 : 5
  2. খ
    5 : 4
  3. গ
    1 : 3
  4. ঘ
    2 : 3
ব্যাখ্যা
Question: An alloy of copper and nickel contains 65% copper. A second alloy contains copper and nickel in the ratio 17 : 3. In what ratio should the two alloys be mixed so that the new mixture contains 4 times as much copper as nickel?

Solution:
First alloy - 65% copper. ∴ 35% Nickel.
Ratio is 65 : 35 = 13 : 7.

2nd alloy,
Ratio is 17 : 3
∴ Proportion of copper in the 1st alloy = 13/20 and
proportion of copper in the 2nd alloy = 17/20.
Also proportion of copper in resulting alloy = 4/5.

Hence required ratio is (17/20 - 4/5) : (4/5 – 13/20) = 1 : 3.
৯৩৩.
The students in Parimal’s class walk, cycle or drive to school in the ratio 2 : 1 : 4. If 8 students walk, how many students are there in Parimal’s class altogether?
  1. ক
    56
  2. খ
    16
  3. গ
    30
  4. ঘ
    28
ব্যাখ্যা
Question: The students in Parimal’s class walk, cycle or drive to school in the ratio 2 : 1 : 4. If 8 students walk, how many students are there in Parimal’s class altogether?

Solution:
Let,
Number of students walk = 2x
Number of student having cycle = x
Number of student driving = 4x
∴ Total number of students = 2x + x + 4x = 7x

ATQ,
2x = 8
∴ x = 4

∴ Number of students = 7 × 4 = 28
৯৩৪.
A can contains a mixture of two liquids A and B in the ratio 5 : 3. When 12 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 5 : 8. How many litres of liquid A was contained by the can initially?
  1. ক
    19.5 litres
  2. খ
    17.5 litres
  3. গ
    23.5 litres
  4. ঘ
    25.5 litres
ব্যাখ্যা
Question: A can contains a mixture of two liquids A and B in the ratio 5 : 3. When 12 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 5 : 8. How many litres of liquid A was contained by the can initially?

Solution:
Let liquids A is initially 5x, liquid B is 3x litres
12 litres of mixture are drawn, remaining mixture A = 5x - (5/8) × 12 = 5x - 7.5
Remaining mixture B = 3x - (3/8) × 12 = 3x - 4.5
After filling, mixture becomes = 3x - 4.5 + 12 = 3x + 7.5
5x - 7.5/3x + 7.5 = 5/8
⇒ (40x - 60)/(24x + 60) = 5/8
⇒ 320x - 480 = 120x + 300
⇒ 200x = 780
⇒ x = 3.9
Liquid A is (5 × 3.9) or 19.5 litres
৯৩৫.
The ratio of the number of sides of a square to the number of edges of a cube is 
  1. ক
    2 : 3
  2. খ
    1 : 3
  3. গ
    1 : 2
  4. ঘ
    1 : 1
ব্যাখ্যা
Question: The ratio of the number of sides of a square to the number of edges of a cube is 

Solution: 
the number of sides of a square = 4
the number of edges of a cube = 12

∴ The ratio of the number of sides of a square to the number of edges of a cube is = 4 : 12
= 1 : 3
৯৩৬.
The ratio of 1/5 to 2/7 is-
  1. ক
    3 : 5
  2. খ
    5 : 7
  3. গ
    3 : 10
  4. ঘ
    7 : 10
ব্যাখ্যা
Question: The ratio of 1/5 to 2/7 is-

Solution: 
Here, 
The ratio of 1/5 to 2/7 = 1/5 : 2/7
= (1/5) × 35 : (2/7) × 35
= 7 : 10
৯৩৭.
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
  1. ক
    4 litres, 8 litres
  2. খ
    6 litres, 6 litres
  3. গ
    5 litres, 7 litres
  4. ঘ
    7 litres, 5 litres
ব্যাখ্যা
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

Solution:
Let the cost of 1 litre milk be Tk. 1

Milk in 1 litre mix. in 1st can = 3/4 litre, C.P. of 1 litre mix. in 1st can Tk. 3/4
Milk in 1 litre mix. in 2nd can = 1/2 litre, C.P. of 1 litre mix. in 2nd can Tk. 1/2
Milk in 1 litre of final mix. = 5/8 litre, Mean price = Tk. 5/8

By the rule of alligation, we have:

⇒ Quantity of 2nd can : Quantity of 1st can = (3/4 - 5/8) : (5/8 - 1/2) = (6 - 5)/8 : (5 - 4)/8 = 1/8 : 1/8 = 1 : 1

∴ Quantity of mixure taken from each can = 12 × (1/2) = 6 litres
৯৩৮.
In a regiment the ratio between the number of officers to soldiers was 3 : 31 before. In a battle 6 officers and 22 soldiers were killed and the ratio become 1 : 13, the number of officers in the regiment before battle was?
  1. ক
    18
  2. খ
    21
  3. গ
    24
  4. ঘ
    27
ব্যাখ্যা
Question: In a regiment the ratio between the number of officers to soldiers was 3 : 31 before. In a battle 6 officers and 22 soldiers were killed and the ratio become 1 : 13, the number of officers in the regiment before battle was?

Solution:
Let, the number of officers and soldiers = 3x, 31x

ATQ,
(3x - 6)/(31x - 22) = 1/13
⇒ 39x - 78 = 31x - 22
⇒ 39x - 31x = - 22 + 78
⇒ 8x = 56
∴ x = 7

So, number of officer before = 3x
= 3 × 7
= 21
৯৩৯.
If 20% of A = 30% of B = 1/6 of C, then A : B : C = ?
  1. ক
    ক) 15 : 10 : 21
  2. খ
    খ) 15 : 10 : 18
  3. গ
    গ) 15 : 8 : 12
  4. ঘ
    ঘ) 15 : 10 : 24
ব্যাখ্যা
Question: If 20% of A = 30% of B = 1/6 of c, then A : B : C = ?

Solution: 
20% of A = 30% of B = 1/6 of c
(1/5)A = (3/10)B = (1/6)C
A/5 = 3B/10 = C/6

∴ A/5 = 3B/10
A/B = 15/10

and,
A/5 = C/6
A/C = 5/6 = 15/18

hence, 
A : B : C = 15 : 10 : 18
৯৪০.
In a 567 liters mixture of milk and water, the ratio of milk to water 7 : 2. To get a new mixture containing milk and water in the ratio 7: 3, the amount of water to be added is-
  1. ক
    81 liters
  2. খ
    63 liters
  3. গ
    49 liters
  4. ঘ
    27 liters
  5. ঙ
    21 liters
ব্যাখ্যা
Question: In a 567 liters mixture of milk and water, the ratio of milk to water 7 : 2. To get a new mixture containing milk and water in the ratio 7: 3, the amount of water to be added is-

Solution:
Quantity of milk in 567 liter of mixture = (7 × 567/9) litres
= 441 litres

Quantity of water = (567 - 441) litres
= 126 litres

Let,
x liter of water be added to become ratio = 7 : 3

According to the question,
7/3 = 441/(126 + x)
⇒ 7(126 + x) = 441 × 3
⇒ 882 + 7x = 441 × 3
⇒ 7x = 1323 - 882
⇒ 7x = 441
⇒ x = 441/7
∴ x = 63

Therefore, 63 liters of water is to be added.
৯৪১.
The present age of john and marry are in the ratio of 6 : 4. Five years ago their ages were ratio of 5 : 3. How old is john now?
  1. ক
    ক) 42
  2. খ
    খ) 36
  3. গ
    গ) 30
  4. ঘ
    ঘ) 24
ব্যাখ্যা

Let, John's present age = 6x,
and, Mary’s present age = 4x
Therefore,
(6x - 5)/(4x - 5) = 5/3
Or, 20x - 25 = 18x - 15
Or,  x = 5
∴ John’s age = 6 × 5 = 30 years

৯৪২.
A dog takes 3 leaps for every 5 leaps of a hare. If one leap of a dog is equal to 3 leap of the hare then find the ratio of the speed of the dog to that of the hare is :
  1. ক
    ক) 8 : 5
  2. খ
    খ) 9 : 7
  3. গ
    গ) 9 : 5
  4. ঘ
    ঘ) 8 : 7
ব্যাখ্যা

Given that,
A dog takes 3 leaps for every 5 leaps of a hare
Therefore,
Dog : Hare = 3 : 5
One leap of a dog is equal to 3 leap of the hare
Therefore,
1 leap of dog = 3 leap of hare
Now the ratio becomes,
Dog : Hare = 3 (3) : 5
Dog : Hare = 9 : 5
Thus the ratio of the speed of the dog to that of the hare is 9 : 5

৯৪৩.
If A and B are in the ratio 3:4 and B and C are in the ratio 12:13, then A and C will be in the ratio.
  1. ক
    3:13
  2. খ
    9:13
  3. গ
    13:9
  4. ঘ
    4:13
ব্যাখ্যা
Question: If A and B are in the ratio 3:4 and B and C are in the ratio 12:13, then A and C will be in the ratio.

Solution:
A and B are in the ratio 3:4 and B and C are in the ratio 12:13.



Another way,
Given, A and B are in the ratio = 3:4 -------(1)
B and C are in the ratio = 12:13.       --------(2)

To combine, make B's value the same (LCM of 4 and 12 is 12).

Thus, multiplying (1) by 3, we get,
 A:B = 9:12
and B:C = 12:13
Equating two ratios, we can achieve
→ A:C = 9:13
৯৪৪.
125 gallons of a mixture contains 20% water. What amount of additional water should be added such that water content be raised to 25%?
  1. ক
    ক) 15/2 gallons
  2. খ
    খ) 13/2gallons
  3. গ
    গ) 9/2 gallons
  4. ঘ
    ঘ) 8(1/3) gallons
ব্যাখ্যা

In the original 125 gallons of mixture, 20% is water.
Hence, no. of gallons of other materials in the mixture: 125 x 80% = 100 gallons
In the new mixture, water makes up 25%, thus 75% is other materials.
As no. of gallons of others is unchanged, 100 gallons = 75% in the new mixture volume.
The total volume of the new mixture is : 100 / 75% = 100/ 0.75 = 133.33 gallons.
∴ Required additional amount of water = 133.3 – 125 = 8.33 = 8(1/3) gallons

৯৪৫.
The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.
  1. ক
    30
  2. খ
    36
  3. গ
    39
  4. ঘ
    40
ব্যাখ্যা
Question : The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.

Solution : 
Given,
Second : Third = 9 : 16
Third : first = 4 : 1
= 16 : 4

So the ratio of Second  :Third : first = 9 : 16 : 4

∴ The second number = (116 × 9/29)
= 36
৯৪৬.
A bottle of whisky contains 40% alcohol. If we replace a part of this whisky by another whisky containing 20% alcohol, the percentage of alcohol becomes 28%. What quantity of whisky is replaced?
  1. ক
    3/5
  2. খ
    3/4
  3. গ
    4/5
  4. ঘ
    2/5
ব্যাখ্যা
Question: A bottle of whisky contains 40% alcohol. If we replace a part of this whisky by another whisky containing 20% alcohol, the percentage of alcohol becomes 28%. What quantity of whisky is replaced?

Solution:

∴ Ratio of first and second whisky in the mixture
= 8 : 12 = 2 : 3

Now, the quantity of whisky replaced is equal to the quantity of the second whisky added.
∴ The quantity of whisky replaced = 3/5
৯৪৭.
The monthly incomes of A and B are in the ratio 4 : 3. Each saves Tk.600. If their expenditures are in the ratio 3 : 2, then what is the monthly income of A?
  1. ক
    ক) 1800 taka
  2. খ
    খ) 2400 taka
  3. গ
    গ) 3000 taka
  4. ঘ
    ঘ) 1200 taka
ব্যাখ্যা
প্রশ্ন: The monthly incomes of A and B are in the ratio 4 : 3. Each saves Tk.600. If their expenditures are in the ratio 3 : 2, then what is the monthly income of A?

সমাধান:
ধরি,
A  এর মাসিক আয় ৪ক টাকা 
B এর মাসিক আয় ৩ক টাকা

A এর খরচ (৪ক - ৬০০) টাকা 
B এর খরচ (৩ক - ৬০০) টাকা

শর্তমতে,
(৪ক - ৬০০)/(৩ক - ৬০০) = ৩/২
বা, ৮ক - ১২০০ = ৯ক - ১৮০০
বা, ৯ক - ৮ক = ১৮০০ - ১২০০
বা, ক = ৬০০

A এর মাসিক আয় = ৪ × ৬০০ টাকা = ২৪০০ টাকা
৯৪৮.
A sample of 50 liters of glycerine is found to be adulterated to the extent of 20%. How much pure glycerine should be added to it so as to bring down the percentage of impurity to 5%?
  1. ক
    150 liters
  2. খ
    160.5 liters
  3. গ
    164 liters
  4. ঘ
    176 liters
ব্যাখ্যা

Question: A sample of 50 liters of glycerine is found to be adulterated to the extent of 20%. How much pure glycerine should be added to it so as to bring down the percentage of impurity to 5%?

Solution: 
Initially, the 50 liters of glycerine is 20% adulterated. So, the pure glycerine in it is 80% of 50 liters.

Amount of pure glycerine initially = 80% of 50 liters
= 0.8 × 50
= 40 liters

Let 'x' represent the amount of pure glycerine that needs to be added to reduce the percentage of impurity to 5%.

The total volume of glycerine after adding pure glycerine will be 50 + x liters

After adding 'x' liters of pure glycerine, the total amount of pure glycerine in the mixture will be 40  + x liters (added).

Now, this total amount of pure glycerine should be 95% of the new total volume (50 liters original + x liters added), as the impurity percentage is to be reduced to 5%.

So, we can set up an equation:

Total amount of pure glycerine = 95% of total volume after adding pure glycerine

40 + x = 0.95 × 50 + 0.95 × x
⇒ 40 + x = 47.5 + 0.95x
⇒ x - 0.95x = 47.5 - 40
⇒ 0.05x = 7.5
⇒ x = 7.5 / 0.05
⇒ x = 150 liters

৯৪৯.
A man bought some rice and wheat for Tk. 490. The ratio of weight of rice and wheat is 8 : 5 and the price equal amount of rice and wheat is in the ratio 3 : 5. The price of total rice = ?
  1. ক
    Tk. 320
  2. খ
    Tk. 240
  3. গ
    Tk. 280
  4. ঘ
    Tk. 200
ব্যাখ্যা
Question : A man bought some rice and wheat for Tk. 490. The ratio of weight of rice and wheat is 8 : 5 and the price equal amount of rice and wheat is in the ratio 3 : 5. The price of total rice = ?

Solution :
Given,
The ratio of weight of rice and wheat is = 8 : 5
The ratio of equal amount of rice and wheat is = 3 : 5

So the ratio of total price of rice and wheat is = 24 : 25
∴Total = 24 + 25
= 49

According to the question,
49 unit = Tk. 490
∴ 1 unit = Tk. 10

∴ Price of total rice = 24 × 10
= Tk. 240
৯৫০.
Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy?
  1. ক
    11:9
  2. খ
    9:11
  3. গ
    3:6
  4. ঘ
    6:3
  5. ঙ
    None of the above
ব্যাখ্যা

A:: - G:S = 40:60
B:: - G:S:C = 35:40:25
New,
G:S= (1×40 + 4×35) : (40×4 + 1×60)
= 180:220
= 18:22
= 9:11

৯৫১.
Tea worth Tk.126 per kg and Tk.135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk.153 per kg, the price of the third variety per kg will be:
  1. ক
    ক) 84.5 tk 
  2. খ
    খ) 184.5 tk 
  3. গ
    গ) 194.5 tk 
  4. ঘ
    ঘ) 224.5 tk 
ব্যাখ্যা
Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution: 
let, price of third variety x tk per kg 
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk
৯৫২.
If X : Y = 13 : 12 and X – Y = 2, then what is value of 2X + 3Y?
  1. ক
    ক) 64
  2. খ
    খ) 124
  3. গ
    গ) 78
  4. ঘ
    ঘ) 44
ব্যাখ্যা
প্রশ্ন : If X : Y = 13 : 12 and X – Y = 2, then what is value of 2X + 3Y?
সমাধান : 
Let the value of X and Y be 13z and 12z
⇒ X – Y = 2
⇒ 13z – 12z = 2
⇒ z = 2

⇒ The value of X = 13z = 26
⇒ The value of Y = 12z = 24
⇒ 2X + 3Y = 52 + 72 = 124

∴ The value of (2X + 3Y) is 124.
৯৫৩.
In a class, the ratio of the number of boys to girls is 6 : 3. What percent of the members of the club are girls?
  1. ক
    33.3%
  2. খ
    50%
  3. গ
    60%
  4. ঘ
    62.5%
  5. ঙ
    None
ব্যাখ্যা
প্রশ্ন: In a class, the ratio of the number of boys to girls is 6:3. What percent of the members of the club are girls?

সমাধান:
দেওয়া আছে,
ছেলে ও মেয়ের অনুপাত = 6 : 3
= 2 : 1

অনুপাতের যোগফল = 2 + 1 = 3

∴ ক্লাবে মেয়ে সদস্যের শতকরা হার = (1/3) × 100
= 33.3%
৯৫৪.
The ratio of sand and scree in a mixture is 41 : 30, while that of scree and cement is in the ratio 6 : 7. What is the ratio of sand and cement in the mixture?
  1. ক
    ক) 40 : 31
  2. খ
    খ) 41 : 35
  3. গ
    গ) 47 : 33
  4. ঘ
    ঘ) 43 : 38
ব্যাখ্যা
প্রশ্ন : The ratio of sand and scree in a mixture is 41 : 30, while that of scree and cement is in the ratio 6 : 7. What is the ratio of sand and cement in the mixture?
সমাধান :
The ratio of the sand and scree = 41 : 30
The ratio of scree and cements = 6 : 7

According to the question

The sand in the mixture = (41 × 6)
⇒ 246

The cement in the mixture = (30 × 7)
⇒ 210

The ratio of sand and cement in the mixture = (246 : 210)
⇒ 41 : 35

∴ The required ratio is 41 : 35
৯৫৫.
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
  1. ক
    8 : 9
  2. খ
    17 : 18
  3. গ
    21 : 22
  4. ঘ
    21 : 25
  5. ঙ
    Cannot be determined
ব্যাখ্যা
Question: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Solution:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
⇒ (120/100) × 7x and (110/100) × 8x
⇒ 42x/5 and 44x/5

∴ The required ratio = 42x/5 : 44x/5 = 21 : 22.
৯৫৬.
Which number when added to each of the numbers 7, 14 and 28 would make the sums to be in continued proportion?
  1. ক
    0
  2. খ
    5
  3. গ
    3
  4. ঘ
    2
ব্যাখ্যা
Question: Which number when added to each of the numbers 7, 14 and 28 would make the sums to be in continued proportion?

Solution:
Let the number to be added is x.

If three numbers a, b, and c are in continued proportion, then,
a/b = b/c
⇒ b2 =  ac ..... (1)

Now,
7 + x, 14 + x, 28 + x

From (1) we get,
∴ (14 + x)2 = (7 + x)(28 + x)
⇒ 142 + 2 × 14 × x + x2 = 7 × 28 + 7x + 28x + x2
⇒ 196 + 35x + x2 = 196 + 28x + x2
⇒ 35x = 28x
⇒ 35x - 28x = 0
⇒ 7x = 0
∴ x = 0
৯৫৭.
If x2 + 9y2 = 6xy, then x : y is-
  1. ক
    ক) 4 : 1
  2. খ
    খ) 2 : 1
  3. গ
    গ) 3 : 1
  4. ঘ
    ঘ) 6 : 1
ব্যাখ্যা
Given that 
x2 + 9y2 = 6xy
x2 + 9y2 - 6xy = 0
x2 + (3y)2 - 2 . x . 3y = 0
(x - 3y)2 = 0
x - 3y = 0
x = 3y 
x/y = 3/1
x : y = 3 : 1
৯৫৮.
A stick is divided in the ratio 4 : 3 : 1. If the smallest part measures 7.5 cm, what is the length of the longest part?
  1. ক
    30 m
  2. খ
    30 cm
  3. গ
    14 cm
  4. ঘ
    22.5 cm
ব্যাখ্যা
Question: A stick is divided in the ratio 4 : 3 : 1. If the smallest part measures 7.5 cm, what is the length of the longest part?

Solution: 
Given, 
The stick is divided in the ratio 4 : 3 : 1. 

Let, 
Broken parts are 4x, 3x and x cm.

ATQ, 
x = 7.5
∴ 4x = 4 × 7.5
= 30 

Therefore, the largest part = 30 cm
৯৫৯.
The ratios of incomes of A and B is 5:4 and the ratio of their expenditures is 3:2. If at the end of the year each save tk 1600,then the income of A is:
  1. ক
    ক) Tk 3400
  2. খ
    খ) Tk 3600
  3. গ
    গ) Tk 4000
  4. ঘ
    ঘ) Tk 4400
ব্যাখ্যা

Let their income be x
and expenditure be y

A's income = 5x
B's income = 4x

A's expenditure = 3y
B's expenditure = 2y

Both saves 1600
Income - expenditure = saves

5x - 3y = 1600 .... (i)
4x - 2y = 1600 .... (ii)
Substract (ii) × 3 from (i) × 2

10x - 6y - ( 12x - 6y ) = 3200 - 4800
10x - 6y - 12x + 6y = - 1600
- 2x = - 1600

x = 800
Putting the value of x in (i)
5x - 3y = 1600
4000 - 3y = 1600
- 3y = - 2400
y = 800

∴ Income of a = 5x = 4000

৯৬০.
For many two numbers m, n ; (m + n) : (m - n) : mn = 7 : 1 : 60. Find the value of 1/m : 1/n 
  1. ক
    ক) 4 : 3
  2. খ
    খ) 8 : 7
  3. গ
    গ) 3 : 4
  4. ঘ
    ঘ) 7 : 8
ব্যাখ্যা
(m+n)/(m−n) = 7x/x
⇒ m/n=4x/ 3x  
Again   mn=12x2
and mn =60x
so, 60x=12x2
⇒ x = 5
=>  m = 20  and n= 15
Hence,    1/m : 1/n = 1/20 : 1/15 = 3 : 4
৯৬১.
A merchant has 1000 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:
  1. ক
    450 kg
  2. খ
    560 kg
  3. গ
    600 kg
  4. ঘ
    720 kg
ব্যাখ্যা

Question: A merchant has 1000 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:
Total quantity of sugar = 1000 kg

Let x kg be sold at 18% profit
Then (1000 - x) kg be sold at 8% profit

Profit from x kg at 18% = 18x/100
Profit from (1000 - x) kg at 8% = 8(1000 - x)/100

Total profit = 14% of 1000 = 14000/100 = 140

According to the question,
18x/100 + 8(1000 - x)/100 = 140
⇒ 18x + 8(1000 - x) = 14000
⇒ 18x + 8000 - 8x = 14000
⇒ 10x = 14000 - 8000
⇒ 10x = 6000
⇒ x = 600

∴ 600 kg of sugar was sold at 18% profit.

বিকল্প সমাধান:
By the rule of alligation,

Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
∴ Quantity of 2nd kind = (3/5) × 1000 = 600 kg

৯৬২.
Armaan and Ghalib started a cafe with Tk. 40000 and Tk. 80000, respectively. Ghalib got married to someone in another town and left after 7 months. But Jishan immediately replaced him with an investment of Tk. 144000. At the end of the year, the business performed well and registered a profit of Tk. 50600.What is Ghalib’s share in this profit?
  1. ক
    ক) Tk. 13800
  2. খ
    খ) Tk. 16100
  3. গ
    গ) Tk. 16500
  4. ঘ
    ঘ) Tk. 16866.67
ব্যাখ্যা

We know,
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment x Time) : (B's investment x Time) = Profit of A : Profit of B

The total value of investment of Arman, Ghalib, and Jishan after 12 months is =
Tk. 40000 x 12 months : Tk. 80000 x 7 months : Tk. 144000 x (12 - 7)months = 480000 : 560000 : 720000
∴ Profit ratio = 240000 : 280000 : 360000 = 6 : 7 : 9
∴ Share of Ghalib = 7/(6 + 7 + 9) x 50600 = Tk. 16100

৯৬৩.
A mixture of 72 kg contains 17 parts A, 3 Parts of B, 4 parts of C. Find the quantity of B?
  1. ক
    ক) 9 kg
  2. খ
    খ) 10 kg
  3. গ
    গ) 12 kg
  4. ঘ
    ঘ) 14 kg
  5. ঙ
    ঙ) 15 kg
ব্যাখ্যা

Parts of B = 72 × (3/24) kg
= 9 kg

৯৬৪.
The sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually, each male gets Tk 4 and a female Tk 3. The number of females is-
  1. ক
    285
  2. খ
    220
  3. গ
    240
  4. ঘ
    280
ব্যাখ্যা
Question: The sum of money is divided among 160 males and some females in the ratio 16 : 21. Individually, each male gets Tk 4 and a female Tk 3. The number of females is-

Solution:
Let the number of females be x.
Then,
(160 × 4)/3x = 16/21
→ 48x = 160 × 4 × 21
→ x = 280
৯৬৫.
The cost of 8 pens and 4 notebooks is equal to the cost of 12 pens and 2 notebooks. Find the ratio between the cost of 1 pen and the cost of 1 notebook.
  1. ক
    3 : 5
  2. খ
    1 : 2
  3. গ
    1 : 4
  4. ঘ
    2 : 5
ব্যাখ্যা
Question: The cost of 8 pens and 4 notebooks is equal to the cost of 12 pens and 2 notebooks. Find the ratio between the cost of 1 pen and the cost of 1 notebook.

Solution:
Let,
The price of 1 pen = x taka
The price of 1 notebook = y taka

ATQ,
8x + 4y = 12x + 2y
⇒ 12x - 8x = 4y - 2y
⇒ 4x = 2y
⇒ x/y = 2/4
⇒ x/y = 1/2
∴ x : y = 1 : 2
৯৬৬.
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:
  1. ক
    Tk. 18
  2. খ
    Tk. 18.5
  3. গ
    Tk. 19
  4. ঘ
    Tk. 19.5
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, 
Quantity of type 1 rice is 2x kg.
Quantity of type 2 rice is 3x kg.
The price per kg of the mixed variety of rice is y taka

∴ Total price of type 1 rice is 15 × 2x = 30x Taka
∴ Total price of type 2 rice is 20 × 3x = 60x Taka

ATQ,
30x + 60x = y(2x + 3x)
⇒ 90x = y × 5x
⇒ y = (90x)/(5x)
∴ y = 18

৯৬৭.
A mixture of milk and water has a total volume of 42 liters, where milk and water are mixed in the ratio 3 : 4. How many liters of milk must be added so that the quantities of milk and water become equal?
  1. ক
    5 liters
  2. খ
    6 liters
  3. গ
    4 liters
  4. ঘ
    8 liters
ব্যাখ্যা

Question: A mixture of milk and water has a total volume of 42 liters, where milk and water are mixed in the ratio 3 : 4. How many liters of milk must be added so that the quantities of milk and water become equal?

Solution:
The ratio of milk to water is 3 : 4
Total portion = 3 + 4 = 7

Quantity of milk = 42 × (3/7) = 18 liters.
Quantity of water = 42 × (4/7) = 24 liters.

Let,
Quantity of milk to be added = x liters

According to the question,
(18 + x) : 24 = 1 : 1
⇒ (18 + x)/24 = 1/1
⇒ 18 + x = 24
⇒ x = 24 - 18
⇒ x = 6

∴ Quantity of milk to be added = 6 liters

৯৬৮.
The ratio between the sale price and the cost price of an article is 7 : 6. What is the ratio between the profit and the cost price of that article?
  1. ক
    1 : 3
  2. খ
    5 : 6
  3. গ
    1 : 6
  4. ঘ
    1 : 2
ব্যাখ্যা
Question: The ratio between the sale price and the cost price of an article is 7 : 6. What is the ratio between the profit and the cost price of that article?

Solution: 
Let C.P. = 6x and S.P. = 7x
Then, gain = x.
∴ Required ratio = x : 6x = 1 : 6
৯৬৯.
If (x + y) : (x - y) = 4 : 1, then (x2 + y2) : (x2 - y2) is equal to -
  1. ক
    ক) 8 : 17
  2. খ
    খ) 17 : 8
  3. গ
    গ) 16 : 1
  4. ঘ
    ঘ) 25 : 9
ব্যাখ্যা

According to the question,
(x + y)/(x - y) = 4
⇒ x + y = 4x - 4y
⇒ 4x - x = 4y + y
⇒ 3x = 5y
⇒ x/y = 5/3
⇒ x2/y2 = 25/9
Now,
⇒ x2 + y2/x2 - y2
= {(x2 /y2) + 1}/{(x2/y2) - 1}
= {(25/9) +1}/{(25/9 - 1}
(34/9) × (9/16)
= 17/8

৯৭০.
In what ratio a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?
  1. ক
    1 : 2
  2. খ
    1 : 3
  3. গ
    1 : 5
  4. ঘ
    1 : 4
  5. ঙ
    None of the above
ব্যাখ্যা
Question: In what ratio a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

Solution:
Let, X contains 30% alcohol strength and
Y contains 50% alcohol strength

According to the question,
(30% of X) + (50% of Y) = 45% of (X + Y)
⇒ 30X + 50Y = 45X + 45Y
⇒ 15X = 5Y
⇒ X : Y = 1 : 3

Alternative Method,
According to the Rule of Allegation,
৯৭১.
Seats for English, History, and Geography in a school are in the ratio 3 : 4 : 6. There is a proposal to increase these seats by 20%, 25%, and 50% respectively. What will be the new ratio of increased seats?
  1. ক
    9 : 10 : 12
  2. খ
    18 : 25 : 45
  3. গ
    12 : 15 : 18
  4. ঘ
    15 : 20 : 30
ব্যাখ্যা
Question: Seats for English, History, and Geography in a school are in the ratio 3 : 4 : 6. There is a proposal to increase these seats by 20%, 25%, and 50% respectively. What will be the new ratio of increased seats?

Solution:
Originally, let the number of seats for English, History and Geography 3x, 4x, 6x respectively.

Number of increased seats are,
⇒ (120% of 3x), (125% of 4x) and (150% of 6x)
⇒ (120/100) × 3x, (125/100) × 4x and (150/100)  × 6x
⇒ 18x/5, 5x, and 9x

∴ New ratio of, English : History : Geography = 18x/5 : 5x : 9x
= 18x : 25x : 45x
= 18 : 25 : 45
৯৭২.
A 42-liter mixture contains milk and water in a 3 : 4 ratio. How much milk should be added to the mixture to make the ratio equal?
  1. ক
    7 liters
  2. খ
    4 liters
  3. গ
    6 liters
  4. ঘ
    8 liters
ব্যাখ্যা

Question: A 42-liter mixture contains milk and water in a 3 : 4 ratio. How much milk should be added to the mixture to make the ratio equal?

Solution:
The ratio of milk to water is 3 : 4
Total portion = 3 + 4 = 7

Quantity of milk = 42 × (3/7) = 18 liters.
Quantity of water = 42 × (4/7) = 24 liters.

Let,
Quantity of milk to be added = x liters

According to the question,
(18 + x) : 24 = 1 : 1
⇒ (18 + x)/24 = 1/1
⇒ 18 + x = 24
⇒ x = 24 - 18
⇒ x = 6

∴ Quantity of milk to be added = 6 liters

৯৭৩.
The ratio between the perimeter and the length of a rectangle is 7 : 2. If the area of the rectangle is 108 square centimeter, what is the perimeter of the rectangle?
  1. ক
    12 cm
  2. খ
    9 cm
  3. গ
    21 cm
  4. ঘ
    42 cm
ব্যাখ্যা
Let, the breadth and the length be x and y.
xy = 108 --- --- --- (1)
and 2(x + y)/y = 7/2
4(x + y) = 7y
4x + 4y = 7y
4x = 3y
x = 3y/4
From (1), we get,
3y/4 × y = 108
y2 = 108 × 4/3 = 144
y = 12
Therefore, breadth, x = 3y/4 = 9
The perimeter of the rectangle = 2(9 + 12) = 42 cm
৯৭৪.
In a bag, there are three types of coins- 1-tk, 50 paise and 25-paise in the ratio of 3 : 8 : 20. Their total value is 372. The total number of coins is
  1. ক
    738
  2. খ
    836
  3. গ
    1002
  4. ঘ
    961
ব্যাখ্যা
Question: In a bag, there are three types of coins- 1-tk, 50 paise and 25-paise in the ratio of 3 : 8 : 20. Their total value is 372. The total number of coins is

Solution:
Ratio of the number of coins of Re. 1, 50 paise and 25 paise = 3 : 8 : 20
Ratio of the values of these coins = 3 : (8/2) : (20/4) = 3 : 4 : 5

Value of 1 tk coins = (3/12) × 372 = 93 tk
Value of 50 paise coins = (4/12) × 372 = 124 tk
Value of 25 paise coins = (5/12) × 372 = 155 tk

Number of coins = 93 + (124 × 2) + (155 × 4)
= 93 + 248 + 620
= 961
৯৭৫.
How many kgs of wheat costing Tk 8 per kg must be mixed with 36 kg of rice costing Tk 5.4 per kg so that 20% gain may be obtained by selling the mixture at Tk 7.2 per kg?
  1. ক
    ক) 10.2 kg
  2. খ
    খ) 10.5 kg
  3. গ
    গ) 10 kg
  4. ঘ
    ঘ) 10.8 kg
ব্যাখ্যা
Question: How many kgs of wheat costing Tk 8 per kg must be mixed with 36 kg of rice costing Tk 5.4 per kg so that 20% gain may be obtained by selling the mixture at Tk 7.2 per kg?

Solution:
Cost Price = (7.2 × 100)/120 = Tk 6
Let, the quantity of wheat of Tk 8 per kg be x

ATQ,
8x + 36 × 5.4 = 6x + 216
⇒ 8x + 210 = 10x + 216
⇒ 8x + 194.4 = 10x + 216
⇒ 2x = 21.6
⇒ x = 10.8
৯৭৬.
At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is-
  1. ক
    22 years
  2. খ
    25 years
  3. গ
    30 years
  4. ঘ
    34 years
ব্যাখ্যা
Question: At present, the ratio of the age of Muna and Riya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Muna’s present age is-

Solution:
Let, Muna’s present age be = 6x years
and Riya’s present age be = 5x years.

After 15 years, Muna’s age be = (6x + 15) years
After 15 years, Riya’s age be = (5x + 15) years

ATQ,
(6x + 15)/(5x + 15) = 9/8
⇒ 48x + 120 = 45x + 135
⇒ 48x - 45x = 135 - 120
⇒ 3x = 15
⇒ x = 5

∴ Muna’s present age = 6x
= 6 × 5) = 30 years
৯৭৭.
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-
  1. ক
    30%
  2. খ
    15%
  3. গ
    20%
  4. ঘ
    10%
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:
A dishonest milkman professes to sell his milk at cost price, but he mixes it with water and gains 25%

We know, 
Profit = SP - CP
Let milk bought (cost price) be 1 litres at Tk. 100 and profit = 25

∴ Selling price = 100 + 25 = Tk. 125

As the selling price of 1 litre was Tk. 100(same as cost)

Quantity sold = 125/100 = 5/4 = 1.25 litre

Hence, water added = 1.25 - 1 = 0.25 litres

∴ Percentage of water = (0.25/1.20) × 100 = 20%

৯৭৮.
If X and Y are in the ratio 13 : 4, and Y and Z in the ratio 13 : 4, then X and Z will be in the ratio-
  1. ক
    169 : 16
  2. খ
    13 : 4
  3. গ
    4 : 13
  4. ঘ
    13 : 16
ব্যাখ্যা
Question: If X and Y are in the ratio 13 : 4, and Y and Z in the ratio 13 : 4, then X and Z will be in the ratio-

Solution: 
X : Y = 13 : 4
⇒ X/Y = 13/4

Y : Z = 13 : 4
⇒ Y/Z = 13/4

 (X/Y) ×  (Y/Z) = (13/4) × (13/4)
⇒ X/Z = 169/16
∴ X : Z = 169 : 16
৯৭৯.
The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
  1. ক
    8
  2. খ
    10
  3. গ
    12
  4. ঘ
    15
ব্যাখ্যা
Question: The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

Solution:
Let,
The number of students is 30x 
The number of teachers is x

ATQ,
(30x + 50)/(x + 5) = 25/1
⇒ 30x + 50 = 25x + 125
⇒ 30x - 25x = 125 - 50
⇒ 5x = 75
∴ x = 15 

∴ The present number of teachers is 15
৯৮০.
A person spends Tk. 8625 in buying some tables at Tk. 875 each and some chairs at Tk.125 each. The ratio of number of chairs to that of tables when the maximum number of tables is purchased - 
  1. ক
    ক) 1 : 4
  2. খ
    খ) 2 : 3 
  3. গ
    গ) 3 : 5 
  4. ঘ
    ঘ) 4 : 3 
ব্যাখ্যা
Question: A person spends Tk. 8625 in buying some tables at Tk. 875 each and some chairs at Tk.125 each. The ratio of number of chairs to that of tables when the maximum number of tables is purchased - 

Solution:
Maximum possible number of tables = 9   [875 × 9 = 7875] 
Number of chairs purchased = (8625 - 7875)/125 = 6

Hence, required ratio = 6 : 9 = 2 : 3
৯৮১.
There is 24% sugar in the 300 mm mixture. If 300 mm water is added to it, then what percentage of sugar is there in the new mixture?
  1. ক
    12%
  2. খ
    7.2%
  3. গ
    6%
  4. ঘ
    10%
ব্যাখ্যা
In 300 mm mixture, amount of sugar = 24% of 300 = 72 mm
If 200 mm water is added to it, total mixture = 300 + 300 = 600 mm
Therefore, amount of sugar percentage = 72/600 × 100% = 12%
৯৮২.
If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio
  1. ক
    3 : 13
  2. খ
    36 : 13
  3. গ
    13 : 9
  4. ঘ
    9 : 13
ব্যাখ্যা
Question: If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio

Solution:
A/B × B/C = 3/4 × 12/13 = 36/52 = 9/13
A : C = 9 : 13
৯৮৩.
The ratio of the present ages of two friends is 3 : 5. After 7 years, the ratio becomes 2 : 3. What will be the ratio of their ages after 10 years?
  1. ক
    31 : 45
  2. খ
    15 : 22
  3. গ
    29 : 43
  4. ঘ
    None of these
ব্যাখ্যা

Question: The ratio of the present ages of two friends is 3 : 5. After 7 years, the ratio becomes 2 : 3. What will be the ratio of their ages after 10 years?

Solution:
Let
The present age of the friend1 = 3x
The present age of the friend2 = 5x

After 7 years, their ages will be,
⇒ (3x + 7)/(5x + 7) = 2/3
 ⇒ 10x + 14 = 9x + 21
 ⇒ 10x - 9x = 21 - 14
∴ x = 7

Present age of friend1 = 3x = 21 years
Present age of friend2 = 5x = 35 years

Now, after 10 years,
friend1 age = 21 + 10 = 31 years
friend2 age = 35 + 10 = 45 years

∴ The ratio of their ages after 10 years,
= 31 : 45

৯৮৪.
The ratio between the ages of Nila and Shila is 5 : 6 respectively. If the ratio between the one-third age of Nila and half of Shila's age is 5 : 9, then what is Shila's age = ?
  1. ক
    ক) 25 years
  2. খ
    খ) 30 years
  3. গ
    গ) 36 years
  4. ঘ
    ঘ) Cannot be determined
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

Let Nila's age be 5x years and
Shila's age be 6x years

((1/3)×5x):((1/2)×6x) = 5:9
⇒ 5x/(3×3x) = 5/9

Thus, Shila's age cannot be determined

৯৮৫.
The ratio of two numbers is 2 : 3. The sum of the numbers is 100. The difference between the two numbers is:
  1. ক
    ক) 15
  2. খ
    খ) 40
  3. গ
    গ) 25
  4. ঘ
    ঘ) 20
ব্যাখ্যা
ধরি,
ছোট সংখ্যাটি 2x 
বড় সংখ্যাটি 3x

প্রশ্নমতে,
2x + 3x = 100
5x = 100
x = 100/5
x = 20

ছোট সংখ্যাটি 2x  = 2 × 20 = 40
বড় সংখ্যাটি 3x = 3 × 20 = 60 

সংখ্যা দুইটির পার্থক্য 60 - 40 = 20
৯৮৬.
How much sugar, costing Tk. 95 per kg, should be mixed with 17 kg of tea priced at Tk. 200 per kg to get a blend worth Tk. 130 per kg?
  1. ক
    34 kg
  2. খ
    30 kg
  3. গ
    28 kg
  4. ঘ
    26 kg
  5. ঙ
    None of the above
ব্যাখ্যা
Question: How much sugar, costing Tk. 95 per kg, should be mixed with 17 kg of tea priced at Tk. 200 per kg to get a blend worth Tk. 130 per kg?

Solution:
Ratio in which tea and sugar should be mixed
= 200 - 130 : 130 - 95
= 70 : 35
= 10 : 5
= 2 : 1

Let x be the quantity at 95/kg.

∴ 2 : 1 = x : 17
⇒ 2/1 = x/17
⇒ x = 34

Hence x = 34 kg.
৯৮৭.
The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?
  1. ক
    ক) 8 : 7
  2. খ
    খ) 7 : 6
  3. গ
    গ) 9 : 8
  4. ঘ
    ঘ) 3 : 4
ব্যাখ্যা
Question: The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

Solution:
A এর বয়স = 44 × (6/11) বছর = 24 বছর
B এর বয়স = (44 - 24) বছর = 20 বছর
8 বছর পর তাদের বয়সের অনুপাত = (24 + 8)/(20 + 8)
= 32/28
= 8/7
= 8 : 7
৯৮৮.
How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg? 
  1. ক
    36 Kg
  2. খ
    42 Kg
  3. গ
    54 Kg
  4. ঘ
    63 Kg
ব্যাখ্যা
Question: How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

Solution:
By the rule of alligation:
C.P. of 1 kg sugar of 1st kind                               C.P. of 1 kg sugar of 2nd kind 

Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. 
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. 
Then,
7 : 3 = x : 27
or x = (7 × 27)/3 = 63 kg.
৯৮৯.
The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is?
  1. ক
    ক) 6 ml
  2. খ
    খ) 11 ml
  3. গ
    গ) 15 ml
  4. ঘ
    ঘ) 9 ml
ব্যাখ্যা

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7

Let x ml of water be added
We get,
4.5/(4.5 + x) = 3/7
⇒ 9/(9 + 2x) = 3/7
⇒ 63 = 27 + 6x
⇒ 6x = 63 - 27
⇒ 6x = 36
⇒ x = 6

Hence 6ml of water is added.

৯৯০.
The ratio of the ages of A and B at present is 3 ∶ 1. Four years earlier the ratio was 4 ∶ 1. The present age of B is-
  1. ক
    12 years
  2. খ
    24 years
  3. গ
    18 years
  4. ঘ
    36 years
ব্যাখ্যা

Question: The ratio of the ages of A and B at present is 3 ∶ 1. Four years earlier the ratio was 4 ∶ 1. The present age of B is-

Solution:
Given that,
Ratio of present ages of A and B = 3 ∶ 1.
Ratio of their ages 4 years ago = 4 ∶ 1.

Let the present ages of A and B be 3x and x, respectively.
Four years ago,
Age of A = 3x - 4
Age of B = x - 4

AQT,
(3x - 4)/(x - 4) = 4/1
⇒ 3x - 4 = 4(x - 4)
⇒ 3x - 4 = 4x - 16
⇒ 3x - 4x = - 16 + 4
⇒ - x = - 12
∴ x = 12

∴ Present age of B = 12 years.

৯৯১.
The milk and water in a mixture are in the ratio 7 : 5. When 15 liters of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is:
  1. ক
    35 litres
  2. খ
    40 litres
  3. গ
    60 litres
  4. ঘ
    96 litres
  5. ঙ
    67 litres
ব্যাখ্যা

Milk : Water
  7   :    5
  7   :    8
---------------
         3 unit

∴ Remember water is added and not milk, so make milk equal but here milk is already equal
3 units = 15 litres
1 units = 5 litres
8 units = 40 litres
Total quantity of water in the new mixture = 40 litres

৯৯২.
In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes. If the ratio of girls to boys in the class is 3 : 4, then what is the fraction of the students in the class having blue eyes?
  1. ক
    11/45
  2. খ
    11/70
  3. গ
    12/33
  4. ঘ
    14/45
ব্যাখ্যা

Question: In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes. If the ratio of girls to boys in the class is 3 : 4, then what is the fraction of the students in the class having blue eyes? 

Solution:
Let the number of girls be x
Since the ratio of the girls to boys is 3 : 4, the number of boys = 4x/3 
Hence, the number of students in the class = x + (4x/3) = 7x/3

We are given that 10% of girls are blue-eyed,
∴ 10% of x = (10/100)x = x/10 
Also, 20% of the boys are blue-eyed,
∴ 20% of 4x/3 = (20/100) × (4x/3) = 4x/15

Hence, the total number of blue-eyed students = (x/10) + (4x/15)
= 11x/30 

Hence, the required fraction = (11x/30)/(7x/3)
= (11 × 3)/(30 × 7)
= 11/70

৯৯৩.
Two vessels A and B contain milk and water mixed in the ratio 4 : 3 and 2 : 3 respectively. What will be the new ratio of milk to water if these two mixtures are mixed together in equal quantities?
  1. ক
    17 : 18
  2. খ
    2 : 3
  3. গ
    19 : 16
  4. ঘ
    20 : 13
ব্যাখ্যা

Question: Two vessels A and B contain milk and water mixed in the ratio 4 : 3 and 2 : 3 respectively. What will be the new ratio of milk to water if these two mixtures are mixed together in equal quantities? Solution:

সমাধান:
ধরি, পাত্র A এবং B এর মিশ্রণের পরিমাণ সমান, অর্থাৎ ১ একক।
পাত্র A তে দুধের পরিমাণ = 4/(4 + 3) = 4/7
পাত্র A তে পানির পরিমাণ = 3/(4 + 3) = 3/7

পাত্র B তে দুধের পরিমাণ = 2/(2 + 3) = 2/5
পাত্র B তে পানির পরিমাণ = 3/(2 + 3) = 3/5

নতুন মিশ্রণে মোট দুধের পরিমাণ = (4/7) + (2/5)
= (20 + 14)/35 
​= 34/35

নতুন মিশ্রণে মোট পানির পরিমাণ = (3/7) + (3/5)
= (15 + 21)/35
​ = 36/35

∴ নতুন অনুপাত = (34/35) : (36/35)
= 34 : 36
= 17 : 18

৯৯৪.
20 litres of a mixture contains milk and water in the ratio 3 : 1 . Then the amount of milk to be added to the mixture so as to have milk and water in ratio 4 : 1 is-
  1. ক
    ক) 10 litres
  2. খ
    খ) 5 litres
  3. গ
    গ) 7 litres
  4. ঘ
    ঘ) 8 litres
ব্যাখ্যা
In 20 litres of mixture
Quantity of milk ⇒ (3/4) × 20  = 15 litres
Quantity of water ⇒ (1/4) × 20 = 5 litres

Let the quantity of milk added be x litres.

According to the question,
⇒ (15 + x)/5 = 4/1
⇒ 15 + x = 4 × 5
⇒ 15 + x = 20
⇒ x = 20 - 15
⇒ x = 5 litres
৯৯৫.
Two containers have mixtures of milk and water, respectively, in the ratios 5 ∶ 2 and 9 ∶ 5. In what ratio should the contents be mixed so that the ratio of milk to water in the final mixture is 2 ∶ 1? 
  1. ক
    1 : 2
  2. খ
    2 ∶ 1
  3. গ
    9 ∶ 14
  4. ঘ
    6 ∶ 13
ব্যাখ্যা
Question: Two containers have mixtures of milk and water, respectively, in the ratios 5 ∶ 2 and 9 ∶ 5. In what ratio should the contents be mixed so that the ratio of milk to water in the final mixture is 2 ∶ 1? 

Solution :
Let,
P unit of the first mixture is added to Q unit of the second mixture.

So, in P unit of first mixture,
Amount of milk present = (5/7) × P = 5P/7
Amount of water present = (2/7) × P = 2P/7

In Q unit of second mixture,
Amount of milk present = (9/14) × Q = 9Q/14
Amount of water present = (5/14) × Q = 5Q/14

ATQ,
{(5P/7) + (9Q/14)}/{(2P/7) + (5Q/14)} = 2/1
⇒ {(10P + 9Q)/14}/{(4P + 5Q)/14} = 2
⇒ 10P + 9Q = 8P + 10Q
⇒ 2P = Q
∴ P : Q = 1 : 2 
৯৯৬.
The ratio of milk and water in a 48 liters mixture is 7 : 5. Find the quantity of milk to be added to the mixture in order to make this ratio 2 : 1.
  1. ক
    ক) 10 liters
  2. খ
    খ) 20 liters
  3. গ
    গ) 16 liters
  4. ঘ
    ঘ) 12 liters
ব্যাখ্যা
Question: The ratio of milk and water in a 48 liters mixture is 7 : 5. Find the quantity of milk to be added to the mixture in order to make this ratio 2 : 1.

Solution:
Here,
Milk = 48 × (7/12) = 28 L
Water = 48 × (5/12) = 20 L

Let x liters milk be added to the mixture.

Then,
(28 + x) : 20 = 2 : 1
⇒ (28 + x)/20 = 2/1
⇒ 28 + x = 40
⇒ x = 12
৯৯৭.
A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.
  1. ক
    600 kg
  2. খ
    500 kg
  3. গ
    400 kg
  4. ঘ
    None of these
ব্যাখ্যা
Question: A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

Solution: 
Let,
The cost price of sugar be tk. x per kg 
∴ Total cost price = Tk. 1000x
The sugar sold at 8% gain by y kg 
The sugar sold at 18% gain by (1000 - y) kg 

Now
{(108xy)/100} + [{118x(1000 - y)}/100] = (114/100) × (1000x)
⇒ (108y)/100 + [{118(1000 - y)}/100] = (114 × 1000)/100
⇒ 108y + {118(1000 - y)} = 114 × 1000
⇒ 108y  + 118000 - 118y = 114000
⇒ 118000 - 114000 = 10y
⇒ 4000 = 10y
∴ y = 400 kg
৯৯৮.
In a mixture of milk and water, the ratio is 4 : 3. If 5 liters of water is added, the new ratio becomes 4 : 4. What was the original amount of milk in the mixture?
  1. ক
    20 liters
  2. খ
    24 liters
  3. গ
    18 liters
  4. ঘ
    28 liters
ব্যাখ্যা

Question: In a mixture of milk and water, the ratio is 4 : 3. If 5 liters of water is added, the new ratio becomes 4 : 4. What was the original amount of milk in the mixture?

Solution:
ধরি, শুরুতে দুধ ছিল = 4x লিটার,
পানি ছিল = 3x লিটার।

এখন 5 লিটার পানি যোগ করলে, নতুন পানি = 3x + 5 লিটার

ATQ,
4x/(3x + 5) = 4/4
⇒ 4x/(3x + 5) = 1
⇒ 4x = 1 × (3x + 5)
⇒ 4x = 3x + 5
⇒ 4x - 3x = 5
⇒ x = 5

∴ দুধের পরিমাণ = 4x = 4 × 5 = 20 লিটার

৯৯৯.
The ratio between the length and the perimeter of a rectangular plot is 1 : 3 . What is the ratio between the length and the breadth of the field? 
  1. ক
    ক) 2 : 5
  2. খ
    খ) 2 : 3
  3. গ
    গ) 2 : 1
  4. ঘ
    ঘ) 2 : 7
ব্যাখ্যা
Let 
The length of a rectangular be l 
The breadth of a rectangular be b

Now 
l/2(l + b) = 1/3
3l = 2l + 2b
3l - 2l = 2b
l = 2b
l/b = 2/1 
l : b = 2 : 1
১,০০০.
Tk. 1500 is divided into three parts in the ratio (2/3) : (3/4) : (5/6), the 2nd part is-
  1. ক
    Tk. 300
  2. খ
    Tk. 430
  3. গ
    Tk. 480
  4. ঘ
    Tk. 500
ব্যাখ্যা
Question: Tk. 1500 is divided into three parts in the ratio (2/3) : (3/4) : (5/6), the 2nd part is-

Solution:
A : B : C = (2/3) : (3/4) : (5/6)
= {(2/3) × 12} : {(3/4) × 12} : {(5/6) × 12}
= 8 : 9 : 10

∴ Sum of the terms of ratio = (8 + 9 + 10)
= 27

So, First part = Tk.{(9/27) × 1500}
= Tk. 500