Bank Math Master

Question: If the average, of a given number, 50% of that number and 25% of the same number is 350, then the number is- 

Solution: 
Let the number be x
According to the question,
⇒ (x + 50% of x + 25% of x)/3 = 350
⇒ (x + x/2 + x/4)/3 = 350
⇒ 7x/12 = 350
⇒ x = (350 × 12)/7
⇒ x = 600

∴ The number is 600

Question: If a man were to sell his chair for Tk. 675, he would lose 25%. To gain 25% he should sell it for:

Solution: 
CP of chair = (100/75) × 675
 = Tk. 900

To gain 25%, SP = (125/100) × 900
       = Tk. 1125

Question: 65% of a number is more than 25% of the number by 160. What is 20% of that number?

Solution: 
Let the number be x
According to question,
(65x/100) - (25x/100) = 160
⇒ (65x - 25x)/100 = 160
⇒ 40x/100 = 160
⇒ x = (160 × 100)/40
⇒ x = 400

But we have to find 20%, so (20/100) × 400 = 80

Question: A bicycle marked at Tk. 4,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:

Solution: 
Marked Price = 4000
SP after first Discount of 20% = 4000 - 20% of 4000 = 3200
SP after second Discount of 10% = 3200 - 10% of 3200 = 2880
Now, the final selling price at cash = 2880 - 5% of 2880 = Tk. 2736

Question: A starts a business with Tk. 3800 and after 4 months, B joins with some capital. At the end of the year, the profit is divided in the ratio 3 : 4. What is B's contribution to the business?

Solution: 
Let the Contribution of B is Tk. x
A invested for 12 months and B invested for (12 - 4) = 8 months

Now
⇒ (3800 × 12)/(x × 8) = 3/4
⇒ (3800 × 12 × 4)/(3 × 8)= x
⇒ x = 7600

∴ Contribution of B to the business is 7600

Question: The cost price of 15 articles is same as the selling price of 25 articles. What is loss percentage?

Solution: 
Let CP of each article be Tk. 25 and SP of each article be Tk. 15
Loss Percentage
={(25x - 15x) × 100}/25x
= (10x × 100 )/25x
= 40%

Question: The cost of an article was Tk.150. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:

Solution: 
Initial Cost = Tk. 150
After 20% increase in the cost, it becomes,
(150 + 20% of 150)
= 150 + 30
= Tk. 180
Now, Cost is decreased by 20%, So cost will become,
(180 - 20% of 180)
= 180 - 36 
=Tk. 144
So, present cost is Tk.144

Question: A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any?

Solution: 
Let cost price of goods = Tk. 100
Market price of goods
=110% of 100
=(110/100)×100
=Tk. 110

After discount selling price of goods
= 90% of 110
= (90/100) × 110
=Tk. 99

Loss = 100 - 99 = Tk. 1

Loss % = (1/100) × 100 = 1%

Question: After successive discount of 12% and 5% an article was sold for Tk.209. What was the original price of the article?

Solution: 
Let the original price x 
Now
95% of 88% of x = 209 
(95/100) × (88/100)  × x = 209 
x = (209 × 100 × 100)/(95 × 88)
x = 250

Question: If 0.07 is x% of 0.7, then the value of x is- 

Solution: 
x% of 0.7 = 0.07
⇒ (x/100) × 0.7 = 0.07
⇒ x = 0.07 × 100/0.70
⇒ x = 10

Question: 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is- 

Solution: 
Let the smaller number be x and larger number be y
According to the question,
80% of x + 4 = 40% of y
80x/100 + 4 = 40y/100
(8x/10)  + 4= 4y/10
(8x + 40)/10 =4y/10 
4y - 8x = 40
y - 2x = 10 --------- (1)
y - x = 85 ----------- (2)
By using (1) and (2), we get
x = 75
y = 160

Now
x + y = 160 + 75 
= 235

Question: A pair of articles was bought for Tk. 35.70 at a discount of 15%. What must be the marked price of each of the articles? 

Solution: 
Selling price =Tk.  35.70
Discount = 15%.

Let the M.P be 100%.
The selling price will be 100% - 15% = 85%
⇒ 85% = 35.70
⇒ 100% = 35.70 × (100/85)
⇒ 100% = Tk. 42

∴ The Marked price is Tk. 42 .
The marked price of each of the articles = 42/2 = 21Tk. 

Question: By selling 90 balls for Tk. 160 a person loses 20%. How many ball pens should be sold for Tk. 96 so as to have a profit of 20%?

Solution: 
S.P of 90 ball pens  = Tk. 160 
C.P of 90 ball pens  = Tk. {160×(100/80)} =Tk. 200 

Desired  S.P of 90 ball pens  = Tk. (120/100) × 200  =  Tk. 240

For Tk. 240 ball pen sold = 90 
For Tk. 96 ball pen sold = (90/240) × 96 
= 36 

Question: In a business, A and C invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested by A and B was 3 : 2. If Tk. 2730 was their profit, how much amount did B receive?

Solution: 
A : B = 3 : 2 = 6 : 4
A : C = 2 : 1 = 6 : 3
A : B : C = 6 : 4 : 3

B's share = (4​/13) × 2730 = Tk. 840

Question: A trader sells an article and loss (25/2)% . The ratio of cost price to the selling price is-

Solution: 
CP = Tk. x 
SP= (175/2)% of x
    = (175/2) × (1/100) × x
    = 7x/8

Required ratio = x : 7x/8
= 1 : 7/8
= 8 : 7 

Question: A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk.  4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 30,000, A receives

Solution: 
Let
C = x.
B = x + 5000
A = x + 5000 + 4000 = x + 9000
Now 
So, x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000
A : B : C = 21000 : 17000 : 12000
              = 21 : 17 : 12

So A's Share = Tk. 30000 × (21/50) =Tk. 12600

Question: A student multiplied a number by 3/5 instead of 5/3. what is the percentage error in the calculation? 

Solution:
Let number is x

Error = (5x/3) - (3x/5)
= (25x - 9x)/15
= 16x/15

Error % ={(16x/15) × (3/5x) × 100}% = 64%

Question: The cost price of an article is 80% of its marked price for sale. How much percent does the tradesman gain after allowing a discount of 12%?

Solution: 
Let
the marked price =Tk. 100
Then the cost price = 80% of 100 = Tk. 80
After allowing 12% discount on MP,
SP become = 100 - (100 × 12)/100
                   = Tk. 88.
% profit = (8 × 100)/80
              = 10%