ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

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

Question: How much water be mixed in 36 litre of milk worth Tk. 4.80 per litre, so that value of mixture is Tk. 3.60 per litre?

Solution:

Ratio of Milk to water will be = 18 : 6,
In 18 litre milk water added = 6 litre
In 1 litre milk water added = 6/18
In 36 litre milk water added = (6/18) × 36 = 12 litres

Question: If annual income from 6% stock at 80 is Tk. 50 more than 7% stock at 120, then the investment is-

Solution:
Let,
The investment is Tk. x

6% stock at 80,
income from Tk. 80 is 6
∴ income from Tk. x is 6x/80

7% stock at 120,
income from Tk. 120 is 7
∴ income from Tk. x is 7x/120

ATQ,
6x/80 - 7x/120 = 50
⇒ 18x - 14x = 50 × 240
⇒ 4x = 50 × 240
∴ x = 3000

Question: How many kg of Sugar at Tk. 50 per kg must a man mix with 25 kg of sugar at Tk. 34 per kg so that by selling the mixture at Tk. 44 per kg he gains 10% on the outlay?

Solution:
Cost price of mixture = (44/110) × 100 = 40


Ratio of sugar of Tk. 50 and Tk. 34 is = 6 : 10 = 3 : 5
∴ sugar of Tk. 50 per kg to be mixed = (3/5) × 25 = 15kg

Question: How much sugar at Tk. 95 a kg should be added to 17 kg of tea at Tk. 200 a kg so that the mixture be worth Tk. 130 a kg.?

Solution:
Ratio in which tea and sugar should be mixed
= 200 - 130 : 130 - 95 = 70 : 35 = 10 : 5 = 2 : 1
Let x be quantity at 95/kg.

∴ 2 : 1 = x : 17
⇒ 2/1 = x/17
⇒ x = 34
hence x = 34 kg.

Question: A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

Solution:
For an income of tk. 5, investment = tk. 100.
For an income of tk. 4, investment = tk. (100/5) × 4 = tk. 80.
Market value of tk. 100 stock = tk. 80.

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.

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.

Question: A man invested Tk. 45000 when he bought Tk. 100 shares at Tk. 150. If 20% dividend is declared, find his annual income.

Solution:
For Tk. 150 he get Tk. 20
∴ For Tk. 1 He get Tk. (20/150)
∴ For Tk. 45000 He get Tk. (20 × 45000)/150
= Tk. 6000

Question: A vessel is full of mixture of spirit and water in which there is 20% of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12%, find the total quantity in the vessel (in ltrs).

Solution:
Let the total mixture be x liters.
It contains 20% spirit i.e. 0.2 of the total mixture.
When 5 liters are drawn off, quantity of spirit removed = 0.2(5) = 1 liters.
Remaining spirit = 0.2x - 1.
Also remaining spirit = 0.12x.

∴ 0.2x - 1 = 0.12x
⇒ 0.08x = 1
⇒ x = 1/0.08
⇒ x = 12.5

Question: How much chicory at Tk. 5 a kg should be added to 20 kg of coffee at Tk. 12 a kg so that the mixture be worth Tk. 7.50 a kg?

Solution:
Ratio in which coffee and chicory should be mixed
= 12 - 7.5 : 7.5 - 5 = 4.5 : 2.5 = 9 : 5.

Let x be quantity at Tk. 5 a kg
∴ 9 : 5 = x : 20
⇒ 5x = 180
⇒ x = 36

Question: How many shares of market value Tk. 25 can be purchased for Tk. 15775?

Solution:
Number of shares that can be purchased = 15775/25 = 631.

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.

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

Question: A man purchased 300 shares of the face value of Tk. 100 each from the market at Tk. 800 per share. If a dividend of 24% is declared, find his earning percent on the investment.

Solution:
Price of 1 share = Tk. 800.
Dividend rate = 24%.

∴ Earning % on investment = (24/800) × 100 = 3%.