Percentage - Aptitude Questions and Answers Part 2

6. For the sale season, a mall first increased the rate of its products by 10% and then offered a discount of 10%. What is the change in the rate of products in comparison to the original?

a. 1%
b. 1.11%
c. 3.5%
d. 5%

Answer: a. 1%

Explanation:

Let original price be 100
Increase of 10% means the price now = 100 + (10% of 100) = Rs. 110
Now decrease of 10% means price now = Rs. 110 - (10% of 110) = 110 - 11 = Rs. 99
So change in price = 100 - 99 = Re. 1
1 is how much percent of 100? It is 1%
So change in price is 1%.


7. The salaries did not rise with inflation. The butter is now 25% costlier. By what percentage should a housewife reduce the consumption, so that her expenditure stays the same?

a. 12.5%
b. 20%
c. 25%
d. 50%

Answer: b. 20%

Explanation:

Let us assume her consumption was 1 kg at a butter price of Rs 100.
Current expense = 1 x 100 = Rs. 100
New price = 125% of Rs. 100 = Rs. 125
What would be new consumption 'C' for expenses to stay same?
C x 125 = 100
C= 0.8kg
So, new consumption is 80% of the old i.e. it is 20% less than old consumption.

Tip:
For such questions -
Always assume the price of unit quantity (1 kg) as a whole, easy to solve number, preferably 100 (because that is how we talk about percentages - 100%, 85%....so on)


8. The cut off for Olympiad exam at school was 40% marks. Raj Scored 20 marks and missed the cut off by 40 marks. What were the maximum marks for the exam?

a. 100
b. 150
c. 200
d. 250

Answer: b. 150

Explanation:

Let maximum marks be M

To pass = 40% of M =40M
100
Y gets 20 marks and fails by 40 marks.
Hence, 20 + 40 =40M
100
∴ M = 150 marks.


9. Talking about their performance at an entrance exam, Friend A said "I scored 10% marks but my score was 30 marks lower than the passing marks". Friend B said, "I scored 40% marks and was 30 marks above the minimum marks required to pass."
What were the maximum marks required for the exam?

a. 200
b. 350
c. 400
d. 500

Answer: a. 200

Explanation:

Maximum marks = M
IMPORTANT - In both cases minimum marks are the same
A gets 10% of M and fails by 30 marks

∴10M+ 30 = minimum marks
100
B gets 40% of M and gets 30 marks more than minimum marks
∴40M- 30 = minimum marks
100
∴10M+ 30 =40M- 30
100100
∴ 30 + 30 =40M-10M
100100
∴30M= 60
100
∴ M = 200


10. After the recent drought, Government offered a 20% subsidy on wheat so that a family of four can easily buy 10 kg more wheat at a expense of Rs. 100/-. Find the original price of a kilogram of wheat?

a. Rs. 1.5
b. Rs. 2.5
c. Rs. 4.5
d. Rs. 5

Answer: b. Rs. 2.5

Explanation:

20% subsidy price means new price = 0.8P
Let us assume that people buy A kg rice in Rs. 100.
With 20% decrease in price, people will buy (A+10) kg rice in Rs. 100.
Expense = Rs. 100 = Price of rice x Quantity of rice
Since, expense is same, we can say that
A x P = (A+10) x 0.8P
∴ A = 0.8A + 8 --------------- (Cancelling 'P' on both sides)
∴ A = 40

Price of rice =100= Rs. 2.5 per kg.
40

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