ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: Coffee worth Tk. 180 per kg and Tk. 210 per kg are mixed with a third variety in the ratio 2 : 1 : 3. If the mixture is worth Tk. 225 per kg, the price of the third variety per kg will be:

Solution:
Let price of third variety be x Tk. per kg
180 × 2y + 210y + x × 3y = 225(2y + y + 3y)
⇒ 360y + 210y + 3xy = 225 × 6y
⇒ 360 + 210 + 3x = 1350
⇒ 570 + 3x = 1350
⇒ 3x = 780
∴ x = 260 Tk.

Question: Which is better investment: 11% stock at 143 or (39/4)% stock at 117?

Solution:
Let investment in each case beTk. (143 × 117)
Income in 1st case = {(11/143) × 143 × 117}
= Tk 1287

Income in 2nd case = [{39/(4 × 117)} × 143 × 117]
= Tk 1394.25

Clearly (39/4)% stock at 117 is better.

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

Question: An investor purchased 100 shares of stock X at tk per share and sold them all a year later at 24 tk per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

Solution:
buying price = price os total shares + brokerage charges on buy price
=100 × (49/8) + 2% of {100 × (49/8)}
= 624.75 tk

similarly selling price = (24 × 100) - 2% of 2400
= 2352 tk

So, Profit = SP - CP
= 2352 - 624.75
= 1727.25 tk

% = (1727.25/624.75) × 100%
= 276 ~ 280%

Question: A mixture of 200 liters of wine and water contains 25% water. How much more water should be added so that water becomes 40% of the new mixture?

Solution:
Number of liters of water in 200 liters of the mixture = 25% of 200 = 1/4 of 200 = 50 liters
Let us Assume that another 'P' liters of water are added to the mixture to make water 40% of the new mixture.
So, the total amount of water becomes (50 + P) and the total volume of the mixture becomes (200 + P)
Thus, (50 + P) = 40% of (200 + P)
⇒ 50 + P = (40/100) × (200 + P)
⇒ 5000 + 100P = 8000 + 40P
⇒ 60P = 3000
∴ P = 50 liters

Question: In what proportion water must be added to spirit to gain 20% by selling it at the cost price?

Solution:
The percentage gain is essentially the ratio of pure spirit to water in the diluted solution. This gain is made because the addition of water increases the volume without increasing the cost, allowing the adulterated spirit to be sold at the original price (the cost price for the pure spirit).
Since the selling price equals the cost price (CP) in this case, the 20% gain represents the proportion of water in the solution.

Therefore, the proportion of spirit to water is 100% : 20% or 5 : 1.

Hence, water should be added to spirit in a 1 ∶ 5 proportion to gain 20% by selling it at the cost price.

Question: Find the annual income obtained by investing Tk 3000 in 5% debentures of face value Tk 100 at Tk 125?

Solution:
The number of debentures purchased = Tk. 3000/125
One debenture will give an income investment of Tk 100 × 5% = Tk 5.
So, total income = 5 × (3000/125) = Tk 120.

Question: An alloy of gold and copper weights 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?

Solution:
Gold in alloy =50 × 80% = 40gm
Copper in alloy =50 × 20% =10gm
Now,
(40 + x)/10 = 90/10
⇒ 40 + x = 90
⇒ x = 90 - 40
∴ x = 50gm

Question: A wants to secure an annual income of Tk. 1500 by investing in 15% debentures of face value Tk. 100 each and available for Tk. 104 each. If the brokerage is 1%, then the sum of money he should invest is -

Solution:
Income on each debenture = 15% of Tk. 100 = Tk. 15
Number of debentures required = 1500/15 = Tk. 100
Cost of each debenture =Tk. (104 + 1% of 104)
= (104 + 1.04)
= Tk. 105.04

∴ Total investment = Tk. (105.04 × 100)
= Tk. 10504

Question: A man invested Tk. 5200 in Tk. 15 shares quoted at Tk. 13. If the rate of dividend be 9%, his annual income is:

Solution:
Number of shares = 5200/13 = 400 shares
Face value = Tk. (400 × 15) = Tk. 6000
Annual income = Tk. (9/100) × 6000 = Tk. 540

Question: A box contains 56 in the form of coins of one tk, 50 paise and 25 paise. The number of 50 paise coins is double the number of 25 paise coins and four times the number of one tk coins. How many 50 paise coins are there in the box?

Solution:
Number of 1-tk coins = x
Number of 50 paise coins = 4x
Number of 25 paise coins = 2x

Ratio of their values = x : (4x/2) : (2x/4) = 2 : 4 : 1
Value of 50-paise coins = (4/7) × 56 = tk 32
Their number = 32 × 2 = 64

ATQ,
(x )(1) + (4x)(1/2) + 2x(1/4) = 56
⇒ x + 2x + (2/x) = 56
⇒ x = 56 × (2/7)
∴ x = 16

No. of 50p coins = 4 × 16 = 64.