Bank Math Master

Question: If the average of a number, 75% of that number, and 50% of the same number is 420, then what is the number?

Solution: 
Let
the number be x

ATQ,
(x + 75% of x + 50% of x)/3 = 420
⇒ (x + 3x/4 + x/2)/3 = 420
⇒ {(4x + 3x + 2x)/4}/3 = 420
⇒ 9x/12 = 420
⇒ x = (420 × 12)/9
⇒ x = 560

∴ The number is 560

Question: If 30% of x = y, then y% of 50 is equal to what percentage of x?

Solution:
Here,
30% of x = y       
⇒ 30x/100 = y
∴ y = 3x/10

Now,
y% of 50 = 50y/100
= 50 × (3x/10) × 1/100
= 15x/100
= 15% of x

Question: Rina and Mina invest Tk. 25,000 and Tk. 35,000 respectively in a partnership. They earned a profit of Tk. 9,000. Find Rina’s share of the profit.

Solution:
Given,
Investment ratio = 25000 : 35000
= 5 : 7

Sum of the ratio's = 5 + 7 = 12

∴ Rina's share = 9000 × (5/12)
= Tk. 3750

Question: A shopkeeper expects a gain of 25% on his cost price. If in a week, his sale was Tk. 1600, what was his profit?

Solution:
Let
the cost price be x

∴ The selling price = {x + (25% of x)}

ATQ,
x + (25% of x) = 1600
⇒ x + (25x/100) = 1600
⇒ x + (x/4) = 1600
⇒ (4x + x)/4 = 1600
⇒ 5x = 1600 × 4
⇒ x = (1600 × 4)/5
∴ x = 1280

∴ Profit = (1600 - 1280) = Tk. 320

Question: A and B started a business by investing Tk. 40,000 and Tk. 60,000 respectively. After 6 months, C joined the business by investing Tk. 80,000. What is the ratio of their profits at the end of the year?

Solution: 
Given,
A invests Tk. 40,000 for 12 months
∴ A’s investment = 40,000 × 12 = 4,80,000

B invests Tk. 60,000 for 12 months
∴ B’s investment = 60,000 × 12 = 7,20,000

C joins after 6 months and invests Tk. 80,000 for 6 months
∴ C’s investment = 80,000 × 6 = 4,80,000

Profit-sharing ratio A : B : C = 4,80,000 : 7,20,000 : 4,80,000
= 2 : 3 : 2 [divide all by 240000 to simplify]

Question: A and B share profits in the ratio 7 : 3. If 12% of the total profit is given to charity and A’s share is Tk. 3080, find the total profit.

Solution:
Let
total profit = Tk. x
∴ Remaining after charity = 88% of x = 22x/25

ATQ,
(22x/25) of (7/10) = 3080
⇒ 154x/250 = 3080
⇒ 154x = 3080 × 250
⇒ x = (3080 × 250)/154
∴ x = 5000

∴ the total profit = Tk. 5000

Question: Jamal started a partnership by investing Tk. 18,000. After 4 months, Hasan joined by investing Tk. x. If at the end of the year the profits are divided equally, find Hasan’s investment.

Solution:
Given,
Jamal invests Tk. 18,000 for 12 months
∴ Jamal’s investment = 18,000 × 12 = 2,16,000

Hasan invests Tk. x for 8 months
∴ Hasan’s investment = 8x

ATQ,
216,000 : 8x = 1 : 1
⇒ 216,000/8x = 1/1
⇒ 8x = 216000
⇒ x = 216000/8
∴ x = 27000

Question: If a man were to sell his bike for Tk. 67500, he would lose 25%. To gain 25% at what price should he sell it?

Solution: 
Let,
the cost price of the bike be x
Selling at Tk. 67,500 causes a 25% loss,

ATQ,
75% of cost price = 67500
⇒ cost price = 67500 ÷ 75%
⇒ cost price = 67500 ÷ (75/100)
⇒ cost price = {67500 × (100/75)}
∴ cost price = Tk. 90000

∴ To gain 25% he should sell it = (125/100) × 90000
= Tk. 112500

Question: A batsman made 100 runs including 10 boundaries and 5 sixes. What percentage of his runs were made by running between the wickets?

Solution:
Given,
Runs from 4s = 10 × 4 = 40
Runs from 6s = 5 × 6 = 30
Total from boundaries = 40 + 30 = 70

Runs by running between the wickets = 100 - 70 = 30

∴ Percent = 30/100 × 100
= 30%

Question: If shoes are bought at prices ranging from Tk. 500 to Tk. 700 and sold at prices ranging from Tk. 650 to Tk. 900, what is the greatest possible profit from selling 8 pairs?

Solution:
Lowest total cost price = 8 × 500 = Tk. 4000
Highest total selling price = 8 × 900 = Tk. 7200
Greatest profit = 7200 − 4000 = Tk. 3200

Question: Meena and Raju started a business with investments of Tk. (2000 + x) and Tk. (3000 + 2x) respectively. After a year, Raju received a profit of Tk. 4800 out of a total profit of Tk. 8000. Find the value of Meena's investment.

Solution:
Given,
Raju’s profit = Tk. 4800
∴ Meena’s profit = Tk. (8000 - 4800)
= Tk. 3200

Given,
Meena : Raju = 3200 : 4800
⇒ (2000 + x) : (3000 + 2x) = 3200 : 4800
⇒ (2000 + x)/(3000 + 2x) = 3200/4800
⇒ (2000 + x)/(3000 + 2x) = 2/3
⇒ 3(2000 + x) = 2(3000 + 2x)
⇒ 6000 + 3x = 6000 + 4x
⇒ 4x - 3x = 6000 - 6000
∴ x = 0

∴ Initial investment of Meena = 2000 + 0 = Tk. 2000

Question: A TV set is marked at Tk. 18,000. During a sale, a customer buys it at Tk. 16,200. what is the discount percentage.

Solution:
Given,
Marked Price = Tk. 18000
Selling price = Tk. 16200

∴ Discount = (18,000 - 16,200) = Tk. 1,800

∴ Discount % = (1800/18000) × 100 = 10%

Question: A fruit seller sells 20 apples for Tk. 900 and suffers a loss equal to the cost price of 5 apples. Find the cost price of one apple.

Solution:
Let,
cost price of 1 apple is = Tk. x
∴ cost price of 20 apples is = Tk. 20x
∴ cost price of 5 apples is = Tk. 5x

We know,
Cost price - Selling price = Loss
20x - 900 = 5x
⇒ 20x - 5x = 900
⇒ 15x = 900
⇒ x = 900/15
∴ x = 60

∴ Cost price of 1 apple is Tk. 60

Question: Fifty percent of a number is 30 less than three-fourth of the same number. Find the number.

Solution:
Let,
the number = x.

ATQ,
50% of x = (3/4) of x - 30
⇒ 50x/100 = (3x/4) - 30
⇒ x/2 = (3x/4) - 30
⇒ (3x/4) - (x/2) = 30
⇒ (3x - 2x)/4 = 30
⇒ x/4 = 30
∴ x = 120

So, the number is 120.

Question: A shopkeeper marks his goods 30% above the cost price and offers a discount of 10% on the marked price. What is his gain percent?

Solution: 
Let,
the cost price (CP) be Tk. 100

Marked Price = 30% more than cost price
= 100 + 30
= 130 Tk.

Discount = 10% of 130
= (10/100) ​× 130
=13 Tk.

Selling Price (SP)= 130 - 13 = 117 Tk.

∴ Profit = SP - CP = 117 - 100 = 17 Tk.

∴ Gain percent = 17%

Question: The price of pulses is reduced by 20%. Due to this reduction, a customer buys 5 kg more pulses for Tk. 500. Find the original price per kg of pulses.

Solution:
Let
Original price of pulses = x Tk/kg.
Original quantity = 500/x​ kg

New price = 0.80x Tk/kg
New quantity = 500/0.80x = 500/(4x/5) = (500 × 5)/4x = 625/x​ kg

ATQ,
625/x - 500/x = 5
⇒ (625 - 500)/x = 5
⇒ 125/x = 5
⇒ x = 125/5
∴ x = 25

Original price of pulses = 25 Tk/kg.

Question: Anisha and Sara started a business by investing Tk. 85000 and Tk. 15000 each. What be will the ratio of profit earned after 2 years between Anisha and Sara respectively?

Solution: 
Given,
Anisha's investment = Tk. 85,000
Sara's investment = Tk. 15,000
Time = 2 years for both

The ratio of profit earned after 2 years between Anisha and Sara respectively = (85000 × 2) : (15000 × 2)
= 170000 : 30000
= 17 : 3