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101.

If X is `30%` of Z and Y is `60%` of Z, then X is what percentage of Y?

Answer» Correct Answer - `50%`
Discussion
102.

The price of wheat has increased by `25 %.` Find the reduction in consumption so that there is no change in the expenditure.

Answer» Correct Answer - `10(5)/(7)%`
Discussion
103.

Express `36%` as a fraction.

Answer» `36 % =(36)/(100) =(9)/(25)`
`:. 36%` as a fraction is `(9)/(25)`
Discussion
104.

The population of a town increases by `25%` annually. If the present population is one crore, then what was the difference between the population 3 years ago and 2 years ago ?A. 2500000B. 1280000C. 1560000D. 2000000

Answer» Correct Answer - B
(i) `25%` increase from 1st year to 2nd year is equal to `20%` decrease from second year to the first year.
(ii) Let `P(1+(r)/(100))^(n)=1` crore, where `r=25%.`
(iii) Find P, when r = 3 and r=2.
(iv) Find the difference in the value of P in both the cases.
Discussion
105.

In the year 2001, the price of article A is `20%` more than the price of article B. In the year 2002, the price of article A is `50%` more than the price of article B. From 2001 to 2002, if the price of A has increased by `50%` by what per cent has the price of B increased?

Answer» Correct Answer - C
(i) Let the price of A and B in 2001 be Rs. 120x and Rs. 100y. The price of A in the same year will be Rs. 120x and Rs. 120y.
(iii) Given that `(150y-120x)/(120x)=50/100` using this, find the ratio of y and x.
(iv) Find `(y-x)/(x)xx100`
Discussion
106.

If X is `3%` of Z and Y is `60%` of Z, then X is what percentage of Y ?A. `30%`B. `50%`C. `100%`D. `60%`

Answer» Correct Answer - B
Given the X is `30%` of Z and Y is `60%` of Z
`thereforeX is (30)/(60)xx100%of Y.`
`i.e., X is 50% of Y.`
Discussion
107.

The percentag increases in the total number of students of a school over that in the previous year. Find the effective percentage increase in the number of students from 1998-1999 to 2000-2001.A. `31.6%`B. `71.6%`C. `62.6%`D. `81.6%`

Answer» Correct Answer - B
Let the number of students in 1998-99 be 100.
Discussion
108.

The ratio of the incomes of P and Q is `5:4.` The ratio of their expenditure is `4:3` The savings of P more then that of Q by `16(2)/(3)%.` What percentage of his income does P spend ?A. `52(2)/(3)%`B. `53(1)/(3)%`C. `54(1)/(3)%`D. `51(2)/(3)%`

Answer» Correct Answer - B
Let the incomes of P and Q be Rs 5x and Rs 4x respectively . Let the expenditure of P and Q be Rs 4y and Rs 3y respectively
Saving of P =Rs(5x-4y)
Savings of Q =Rs(4x-3y)
`therefore 5x-4y=(4x-3y)(1+(16(2)/(3))/(100))`
`implies 5x-4y =(4x-3y)((7)/(6))`
`implies 30x-24y=28x-21y`
`implies 2x=3y`
Required percentage `=(4y)/(5x)(100)`
`=(4)/(3)((2)/(3))(100)=53(1)/(3)%`
Discussion
109.

The price of an article increases by `10%, 15%and 20%` in 3 consecutive weeks. What is the appeoximate overall percentag increase for the 3 weeks ?A. `45%`B. `62%`C. `35%`D. `52%`

Answer» Correct Answer - D
Let the original price be Rs. 100.
Discussion
110.

When the price of an article is increased by `15%` the number of articles aold decreases by `20%` What is the percentage change in the sales revenue? (Sales revenue = piece of each article X number of articles sold).A. `5%` increaseB. `3%` decreaseC. `8%` increaseD. `8%` decrease

Answer» Correct Answer - D
(i) Let the original price be Rs. 10x and the number of articles sold be 10y.
(ii) Assume the price of each article as Rs. 100 and number of articles as 100.
(iii) Now, price of each article is Rs.115 and the number of articles sold is 80.
(iv) Now, find the sales revenues initially and after the change.
Discussion
111.

The proce of an article increased successively over three consecutive weeks. It increased by `10%` in the first week, `20%` in the second week and `25%` in the third week. Find the effective percentage increase in its price after three weeks.A. `55%`B. `65%`C. `50%`D. `60%`

Answer» Correct Answer - B
Let the initial price be Rs. 100.
Final price (in Rs.) `=100(1+(10)/(100))(1+(20)/(100))(1+(25)/(100))=100((11)/(10))((6)/(5))((5)/(4))`
`therefore ` Effective percentage increase =65%
Discussion