ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: An investor bought 40 shares of Tk 100 each at Tk 125 per share. If the dividend is 6%, what is the yield percent?

Solution:
- Calculate Total Investment (মোট বিনিয়োগ):
Purchase price per share = Tk 125
Number of shares = 40
Total investment = 125 × 40 = Tk 5,000

- Calculate Annual Dividend (বার্ষিক লভ্যাংশ):
Dividend is paid on face value (not purchase price).
Face value = Tk 100/share
Dividend rate = 6%
Dividend per share = 100 × 6% = Tk 6/share
Total dividend for 40 shares = 40 × 6 = Tk 240/year

- Calculate Yield Percentage (লাভের শতকরা হার):
Yield% = (Annual Dividend / Total Investment) × 100
= (240 / 5,000) × 100
= 4.8%

Question: In what ratio should milk costing Tk 40 per litre be mixed with milk costing Tk 60 per litre to get a mixture worth Tk 50 per litre?

Solution:
Use the allegation method:
Cheaper = 40, Costlier = 60, Mean = 50
=> Ratio = (60 – 50):(50 – 40) = 10:10 = 1:1

Alternative:
Let Tk 40 per liter is consists of x liters,
Tk 60 per liter is conists of y liters.
total milk = (x+y) liters
and price of mixture is 50 tk per liter

Now,
→ 40x + 60y = 50(x + y)
→ 40x + 60y = 50x + 50y
→ 10y = 10x
→ x : y = 1 : 1

Question: A person wants an annual income of Tk 2,400 from a stock paying 8% dividend. If the market price of the Tk 100 stock is Tk 120, how much should he invest?

Solution:
→ Calculate Dividend per Share (প্রতি শেয়ারে লভ্যাংশ):
Dividend is paid on face value, not market price.
Dividend per share = Face value × Dividend rate
= Tk 100 × 8%
= Tk 8/share/year.

→ Determine Number of Shares Needed (প্রয়োজনীয় শেয়ার সংখ্যা):
To earn Tk 2,400/year with Tk 8/share/year:
Number of shares = Total desired income ÷ Dividend per share
= 2,400 ÷ 8
= 300 shares.

→ Calculate Total Investment (মোট বিনিয়োগ):
Each share costs Tk 120 (market price).
Total investment = Number of shares × Market price
= 300 × Tk 120
= Tk 36,000.

Question: A shopkeeper mixes 3 litres of water with 15 litres of milk costing Tk 60 per litre and sells the whole at cost price. What is the profit percentage?

Solution:
→ Total cost = 15 × 60 = Tk 900
→ Total volume = 18 litres, Selling price per litre = 900/18 = Tk 50
→ Profit per litre = 60 – 50 = Tk 10
→ Profit % = (10/50)×100 = 20%

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: In 60 litres of mixture, milk and water are in 3 : 2. How much water to add to make it 1 : 1?

Solution:
Find the quantity of milk and water in the initial mixture:
→ Total parts = 3 + 2 = 5 parts
→ Milk = (3/5) × 60 = 36 L
→ Water = (2/5) × 60 = 24 L

Let x liters of water be added.
New amount of water = 24 + x
Milk remains the same = 36 L

According to the question:
We want the final ratio to be 1:1, i.e.
→ Milk = Water
⇒ 36 = 24 + x
⇒ x = 36 − 24 = 12 L

Question: By investing Tk. 1500 in a 10% stock , a man obtains an income of Tk. 150. Find the market price of the stock. 

Solution:
To earn Tk. 150 investment = Tk. 1500
To earn Tk. 10 investment = Tk. (1500 × 10)/150
= Tk. 100

Question: From 50 L wine, 10 L is removed and replaced with water. Process repeated twice. Wine left = ?

Solution:
A container has 50 liters of wine.
Each time, 10 liters of wine is removed and replaced with water.
This process is done twice.

After first removal of 10 L wine 
Wine left = 40
Water added 10 L
Total 50 L
Wine part = 40/50= 4/5
Water part = 1/5
Now, again 10 liters of wine is removed 
Wine removed = (4/5)×10 = 8
Water removed = (1/5) × 10 = 2

After removal:
Wine left = 40- 8 =32 L
Water left = 10- 2 = 8 L
10 L water added 
New water = 18 L
and Wine Left = 32 L

Question: Which is the better investment: 9% stock at Tk 90 or 12% stock at Tk 120?

Solution:
→ Yield of 9% stock = (9 / 90) × 100 = 10%
→ Yield of 12% stock = (12 / 120) × 100 = 10%
On every taka you put in, both give the same 10 % return.
correct answer: Both are same

Question: How much water must be added to 20 L of 30% salt solution to make it 20%?

Solution:
Total solution 20 L
30% salt solution has salt of = (20×30)/100 = 6 L

Now,
Let the amount of water to be added to make 20% salt solution = x liters
Then, new total solution = 20 + x
Salt remains = 6 L

New salt percentage = 
→ 400+ 20x= 600
→ 20x= 200
→ x= 10

Question: A man bought 40 shares of Tk 100 each at Tk 95 and sold them at Tk 110. What is his total gain?

Solution:
→ Buying price = 40 × 95 = Tk 3,800
→ Selling price = 40 × 110 = Tk 4,400
→ Profit = 4400 − 3800 = Tk 600

Question: A merchant has 1000kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% overall. The quantity sold at 18% profit is-

Solution:
Let the sugar sell at 18% profit is = x
So, the sugar sell at of 8% profit = 1000-x

According to question,
18% of x + 8% of (1000 -x) = 14% of 1000
→ 18x/100 + (8000 - 8x)/100 = 14000/100
→ 18x + 8000 - 8x = 14000 (multiplying both sides by 100)
→ 10x = 6000
→ x = 600 kg

Question: A and B are two alloys of gold and copper prepared by mixing metals in the ratios 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C will be -

Solution: A and B are two alloys of gold and copper prepared by mixing metals in the ratios 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C

 Gold in C


Copper in C 


∴ Gold: Copper = 7/6:5/6 = 7:5

Question: Fresh grapes contain 80% water by weight, while dry grapes contain only 20% water. If a person has 100 kg of fresh grapes, how many kilograms of dry grapes can be obtained from them after drying?

Solution:
Fresh grapes: 80% water → 20% solid
So, in 100 kg fresh grapes:
Water = 80 kg
Solid = 20 kg
When grapes dry, water evaporates, but the solid remains unchanged.

Dry grapes: 20% water → 80% solid
That means the 20 kg solid must now be 80% of the dry grape weight
So, let total weight of dry grapes = x

Then:
0.8x=20
⇒x=200/0.8 =25 kg

Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

Solution: Let Gold is 19x times as heavy as water and copper is 9y times as heavy as water.

Now, 
→ 19x+ 9y = 15(x+y)
→ 19x+ 9y = 15 x+ 15y
→ 4x= 6y
→ x:y =6:4
→ x:y = 3:2