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Important Formulae

What is Percentage?
When we say "Percent" we are really saying "per 100", written as x%.

To express x% as a fraction:
We have, x% = x/100
Thus, 10% = 10/100 = 1/10
To express a/b as a percent:
We have, a/b = (a/b X 100)%.

Thus, 1/5 = (1/5 X 100)%. = 20%.

Percentage Increase/Decrease:

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

[R/(100 + R) X 100]%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

[R/(100 - R) X 100]%

Results on Population:

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:

1. Population after n years = P[1 +R/100]n
2. Population n years ago =P/(1 +R/100)n

Results on Depreciation:

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:

1. Value of the machine after n years = P[1 - R/100]n
2. Value of the machine n years ago = P/(1 - R/100)n
3. If A is R% more than B, then B is less than A by = [R/(100 + R) X 100]%
4. If A is R% less than B, then B is more than A by = [R/(100 - R) X 100]%

Practice Questions

1.

The strength of school increased by 10% this year. By what percent was the strength less last year, when compared to this year?
A.10%B.11%
C.111/9%D.91/11%

Report! Answer!

Answer is: D

Let, last year the strength was 100.
This year it is 110.
Last year, it was (10/110) X 100% = (1/11) X 100% = 100/11%
i.e., 91/11% , less than this year.

2.

A's weight is 10% less than that of B and C's weight is 10% more than that of B. By what percent is A's weight less than that of C?
A.20%B.182/11%
C.19/11%D.162/3%

Report! Answer!

Answer is: B

Let B's weight be 100
A's weight is 90
C's weight is 110
So, A's weight is (20/110) X 100%
A's weight = (2/11) X 100% = (200/11)%
A's weight = (182/11)% less than that of C.

3.

A salesperson used to get a commission of 9% of his total sales for a month. With a change in the terms of employment, he now gets a fixed amount of ?3000 per month plus a commission of only 5% on the excess of his sales over ?10,000. If the difference in the amounts that he received last month and this month and this month is ?400, though the total sales were the same, what were the total sales this month?
A.57,500B.52,500
C.67,500D.Cannot be determined

Report! Answer!

Answer is: D

Case 1:
New scheme income - old scheme income = 400
3000 + 5/100(S - 10000) - 9/100(S) = 400
2500 - 0.04S = 400
S =2100/0.04
S = 52500
Case 2:
Old scheme income - new scheme income = 400
9/100(S) - [3000 + 5/100(S-10000)] = 400
(0.04)S - 2500 = 400
0.04S = 2900
S = 72500
Since we have two possible answers satisfying the required conditions, we cannot determine the answer uniquely.

4.

Four teachers , five students and two members of the non-teaching staff went as a group on a visit to temple. They contributed the following amounts towards the expenses. The teachers contributed Rs 100 each, the students Rs 30 each and the non-teaching staff Rs 25 each. What percent of the total expenditure did each student pay?
A.162/3%B.4%
C.41/6%D.5%

Report! Answer!

Answer is: D

The teachers contribution = 4 X 100 = 400
Students contribution = 5 X 30 = 150
The contribution of non-teaching staff = 2 X 25 = 50
Total contribution = Rs 600
Contribution of each student = (30/600) X 100%
Contribution of each student = (1/20) X 100% = (100/20)% = 5%

5.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
A.588 applesB.600 apples
C.672 applesD.700 apples

Report! Answer!

Answer is: D

Suppose originally he had x apples.
Then, (100 - 40)% of x = 420
(60/100)x = 420
x = (420 X 100)/60 = 700 apples.

6.

Hari has just enough money to buy 50 papayas or 30 watermelons. He decides to spend only 90% of his money and buy 9 watermelons. How many papayas can he buy with the remaining money that he wants to spend?
A.45B.30
C.25D.15

Report! Answer!

Answer is: A

Let the cost of 50 papayas or 30 watermelons be Rs 150.(money with Hari)
So, each papaya costs Rs 3 and each watermelon costs Rs 5.
Let him buy x papayas and 9 watermelons for Rs 135 (90% of his money)
3x + 45 = 135
x = 30

7.

Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.Rs. 15B.Rs. 15.70
C.Rs. 19.70D.Rs. 20

Report! Answer!

Answer is: C

Let the amount taxable purchases be Rs. x.
Then, 6% of x = 6/100
x = [30/100 X 100/6] = 5
Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

8.

If 10% of a is b% of 200, a/b = ?
A.20B.1/20
C.10D.1/10

Report! Answer!

Answer is: A

10/100a = b/100 (200)
a/b = 20

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