ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: 600 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 75% in the solution?

Solution:
Amount of sugar =600 × 30/100
=180 grams
Let,
x gram sugar to be added

ATQ,
(180 + X)/(600 + X) = 75%
⇒ (180 + X)/(600 + X) = 75/100
⇒ (180 + X)/(600 + X) = 3/4
⇒ 4(180 + X) = 3(600 + X)
⇒ 4X + 720 = 3X + 1800
⇒ 4X - 3X= 1800 - 720
∴ X = 1080 grams

Question: Two partners invest TK 1,00,000 and TK 60,000 .After 6 months, they admit a new partner with TK 80,000. What is the ratio of their profits after one year?

Solution:
Profit sharing ratio depends on : Capital × Time
Let,
the partners be P, Q and R

P's invest : TK 1,00,000 for 12 months
⇒ 1,00,000 × 12 = 12,00,000

Q's invest : TK 60,000 for 12 months

⇒ 60,000 × 12 =7,20,000

R's invest: TK 80,000 for 6 months

⇒ 80,000 × 6 = 4,80,000

Now, the ratio of profits:
12,00,000 : 7,20,000 : 4,80,000

Simplify = 5 : 3 : 2

∴ Ratio = 5 : 3 : 2

Question: A grocer mixes two types of pulses, one costing 20 taka per kg and the other 25 taka per kg.If the mixture is sold at 22 taka per kg, what is the ratio of two types of pulses in the mixture?

Solution:
মনে করি,
প্রথম প্রকার ডালের পরিমাণ = x কেজি
দ্বিতীয় প্রকার ডালের পরিমাণ = y কেজি

প্রথম প্রকার ডালের x কেজির মূল্য = 20x টাকা
দ্বিতীয় প্রকার ডালের y কেজির মূল্য = 25y টাকা

প্রশ্নমতে,
20x + 25y = 22(x + y)
⇒ 20x + 25y = 22x + 22y
⇒ 22x - 20x= 25y - 22y
⇒ 2x = 3y
∴ x/y = 3 : 2

Question: Rana and Rahim invest TK 30,000 and 40,000 respectively in a partnership. They earned a profit of TK 7000. Find Rana's share of the profit.

Solution:
Given that,
Investment ratio = 30,000 : 40,000
= 3 : 4

sum of  the ratio's = 3 + 4 = 7
∴ Rana's share of the profit = 7000 × (3/7)
= 1000 × 3
= 3000 tk

Question: If 2 (P's capital) = 5 (Q's capital) = 6 (R's capital), then out of the total profit of TK 6500, Q will receive-

solution:
Let,
P's capital = p
Q's capital = q
R's capital = r

Then,
2p = 5q = 6r

⇒ q = 2p/5

⇒ r = 2p/6 = p/3

P : Q : R = p : 2p/5 : p/3
= 15p : 6p : 5p [multiply by 15]
= 15 : 6 : 5

∴ sum of ratio = (15 + 6 + 5) = 26

so, Q's share = 6500 × 6/26 = 250 × 6 = 1500 TK

Question: A, S and D Started a business with the investment of TK 5000, TK 4000 and TK 3000 respectively. At the end of the year, the profit received by S and D together is TK 2000 more than  the profit received by A. What is the total profit of the business?

Solution:

বিনিয়োগের অনুপাত, A : S : D = 5000 : 4000 : 3000
= 5 : 4 : 3

মনে করি,
মোট লাভ p টাকা
∴ A এর লাভ = 5p/12

S এবং D এর লাভ একত্রে = (4P/12) + (3P/12) = 7p/12

প্রশ্নমতে,
7p/12 = (5p/12) + 2000
or, (7p/12 ) - (5p/12) = 2000
or, (7p - 5p)/12 = 2000
or, 2p/12 = 2000
∴ p = 12000

মোট লাভ 12000 টাকা 

Question: If A : B = 3 : 4, B : C = 5 : 6, and C : D = 7: 9 then A : D is equal to-  

Solution:
Given that,
A : B = 3 : 4, B : C = 5 : 6, and C : D = 7: 9
Then,
A/D = (A/B) × (B/C) × (C/D)
= (3/4) × (5/6) × (7/9)
= 35/72
= 35 : 72
∴ A : D = 35 : 72

Question: 20 litres of a mixture contains milk and water 4 : 1. Then the amount of water to be added to the mixture so as to have milk and water in ratio 2 : 1 is-

Solution:
In 20 litres of mixture,
quantity of mik = 20 × (4/5) = 16 litres
quantity of water = 20 × (1/5) = 4 litres
Let,
The quantity of water be added m litres
ATQ,
16 : (4 + m) = 2 : 1
or, 16/(4 + m) = 2/1
or, 2m + 8 = 16
or, 2m = 16 - 8
or, 2m = 8
∴ m = 8/2 = 4

∴ 4 litres water to be added to the mixture.

Question: A working partner receives a commission equal to 30% of the profit remaining after paying his commission. If his commission is Tk 12,000, find the total profit.

Solution:
Let,
the total profit be K taka
According to the question,
remaining profit after paying 30% working partners commission = (K - 12000)

∴ (K - 12000) × (30/100) = 12000
⇒ (K - 12000) = 12000 × (100/30)
⇒  (K - 12000) = 40,000
⇒ K = 40,000 + 12,000
∴ K = 52,000

so, Total profit = 52,000 TK

Question: The ratio of P : Q is 3 : 4 and the ratio of Q : R is 5 : 6. If P is equal to 9, what is the value of R?
Solution:
Given that,
P : Q = 3 : 4
Q : R = 5 : 6
And P = 9

Now,
P : Q = 3 : 4
or, P/Q = 3/4
or, 9/Q = 3/4
or, 3Q = 36
or, Q = 36/3
∴ Q = 12

And,
Q : R = 5 : 6
or, Q/R = 5/6
or, 12/R = 5/6
or, 5R = 72
or, R = 72/5
∴ R = 14.4

so, the value of R is 14.4

Question: Rina ,Ratul and Ayesha started a business. Rina invested 1/3 part, Ratul 1/4 part and rest of the capital was invested by Ayesha. The ratio of their profits will be-

Solution:
Let,
Total capital be TK x
Then,
Rina's share = x/3 TK
Ratul's share = x/4 TK
Ayesha's share = x - {(x/3) + (x/4)}
= x - {(4x + 3x)/12}
= x - (7x/12)
= (12x - 7x)/12
= 5x/12 TK

∴ Required ratio
= (x/3) : (x/4) : (5x/12)
= 4x : 3x : 5x     [multiply by 12]
= 4 : 3 : 5

Question: A shopkeeper has two varieties of lentils priced at Taka 60 per kg and Taka 80 per kg. In what ratio should he mix them to get a mixture worth Taka 68 per kg?

Solution: 
Cheaper variety price of lentils, p = 60 Taka
Expensive variety price of lentils, q = 80 Taka
mixture price, r = 68 Taka

Ratio = (q - r)/(r - p)
=(80 - 68)/(68 - 60)
=12/8
= 3 : 2

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

Question : A starts a business with Tk 4,500. After 4 months, B joins as a partner by investing some amount. At the end of one year from the start, the profits are shared in the ratio A : B = 3 : 4. Find B’s capital investment.

Solution:
Let,
B's capital be TK X
Then,
(4500 × 12)/8X = 3/4
⇒ 24X = (4500 × 12 × 4)
⇒ 24X = 216,000
⇒ X = 216,000/24
∴ X = 9000

Question: The ratio of the number of boys and girls in a school is 7 : 4. If the percentage increase in the number of boys and girls be 25% and 15% respectively, what will be the new ratio?

Solution: 
Let,
The number of boys and girls in a school be 7X and 4X respectively
their increased number number is (125% of 7X) and (115% of 4X)
⇒ (125/100) of 7X and (115/100) of 4X
⇒ 35X/4 and 23X/5

∴ required ratio = 35X/4 : 23X/5
= 175X : 92X        [multiply by 20]
= 175 : 92

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

Question: A man invested TK 4500 in a stock at 108 to obtain an income of TK 250. What is the dividend from the stock?

Solution:
By investing TK 4500, income  = TK 250
By investing TK 108 = (108 × 250)/4500 = 6

Hence, the dividend is 6%.

Question: Junayed starts a business with TK 9000 and after one year, Rayhan joins with junayed by investing a certain amount. At the end of 2 years, If 3 : 2 is the proportion of the profit then Rayhan's contribution to the capital is-

Solution:
Let,
Rayhan's capital be TK P
Junayed's investment = TK 9000 for 24 months
Rayhan's investment = TK p for 12 months
we know that, profit ratio = investing ratio

ATQ,
(9000 × 24)/(p × 12) = 3 : 2
or, (9000 × 24) : 12p = 3 : 2
or, (9000 × 24)/12p = 3/2
or, 36p = (2 × 24 × 9000)
or, p = (48 × 9000)/36
∴ p = 12000

The required answer is 12000 TK 

Question: To produce an annual income of TK 800 from a 8% stock at 80, the amount of stock needed is-

Solution:
since face value is not given, take it as TK 100
As it is a 8% stock, income(dividend) per stock = TK 8
ie, For an income of TK 8, the amount of stock needed = TK 100
For an income of TK 800, the amount of stock needed = (100 × 800)/8 = 10,000

Question: A and B invest in a business in the ratio 7 : 3. If 20% of the total profit goes to charity and B's share is TK 12000, the total profit is-

Solution: 
মনে করি,
মোট লাভ 100 টাকা
20% দান করার পর থাকে = (100 - 100 এর 20%) = 80 টাকা

80 টাকার মধ্যে B পাবে = 80 × (3/10) = 24 টাকা

24 টাকা পায় যখন মোট লাভ 100 টাকা
∴ 12000 টাকা পায় যখন মোট লাভ = (12000 × 100)/24 = 50,000 টাকা 

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  

Question: A Vessel is filled with liquid, 3 parts of which are water and 4 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
মনে করি,
পাত্রের মিশ্রণের পরিমাণ ৭ লিটার

মিশ্রণে পানির পরিমাণ ৩ লিটার
মিশ্রণে সিরাপের পরিমাণ  ৪ লিটার

পাত্রের পানি ও সিরাপের পরিমাণ অর্ধেক অর্ধেক করতে ক লিটার মিশ্রণ অপসারন করে পানি দিতে হবে।

ক লিটার মিশ্রণে পানির পরিমাণ ৩ক/৭ লিটার
ক লিটার মিশ্রণে সিরাপের পরিমাণ ৪ক/৭ লিটার

পানি মিশানোর পর,
নতুন মিশ্রণে পানির পরিমাণ হবে {(৩ - ৩ক/৭) + ক} লিটার
= (২১ + ৪ক)/৭ লিটার
নতুন মিশ্রণে সিরাপের পরিমাণ হবে (৪ - ৪ক/৭) লিটার
= (২৮ - ৪ক)/৭ লিটার

শর্তানুযায়ী,
(২১ + ৪ক)/৭ = (২৮ - ৪ক)/৭ 
বা, ২১ + ৪ক = ২৮ - ৪ক
বা, ৪ক + ৪ক = ২৮ - ২১
বা, ৮ক = ৭
∴ ক = ৭/৮

৭ লিটার মিশ্রণ ৭ লিটারের ১ বা সম্পূর্ণ অংশ
∴ ৭/৮ লিটার মিশ্রণ ৭ লিটারের (৭/৮)/৭ অংশ
= ১/৮ অংশ

Question: The contributions made by Rasel and Akash are in the ratio of 6 : 4. If 10% of the total profit is donated and Rasel gets 9000 as his share of profit, what is the total profit?

Solution:
Let,
the total profit after donated = p
The ratio of contribution by Rasel and Akash = 6 : 4
sum of ratios = 10

Rasel's share = (6/10) × p = 9000
⇒ p = (10 × 9000)/6
∴ p = 15000
so, total profit after donated = 15000

ATQ,
Rasel gets 9000 after 10% donated
Now,
90% = 15000
1% = 15000/90
And, 100% = (15000 × 100)/90 = 16,666.66

Question: A stock increases in value by 20%. By what percent must the stock decrease to reach back to its former value?

Solution:
এখানে,
20% বৃদ্ধিতে মূল্য = (100 + 20) = 120 টাকা

120 টাকায় মূল্য কমাতে হবে 20 টাকা
∴ 1 টাকায় মূল্য কমাতে হবে 20/120
∴ 100 টাকায় মূল্য কমাতে হবে (20 × 100)/120
= 16.66 টাকা

Question: The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio of 9 : 7. If each saves BDT 50 per month, what would be the total amount of their monthly expenditure?

Solution:
Let,
Their monthly income 5a and 4a
Their monthly expenses 9b and 7b

ATQ,
5a - 9b = 50 ..............(1)
4a - 7b = 50 ...............(2)

Multiply equation (1) and (2) by 4 and 5 respectively,
20a - 36b = 200 .............(3)
20a - 35b = 250 ..............(4)

(3) - (4) ⇒
20a - 36b- 20a + 35b = 200 - 250
or, - b = - 50
∴ b = 50

Hence, their total monthly expenditure = 9 × 50 + 7 × 50 = 450 + 350 = 800 tk