# Percentages Quiz Set 012

### Question 1

A number is first increased by 100%. By what percent must it be reduced so as to restore it to its previous value?

A

50 %.

B

51 %.

C

49 %.

D

\$17{2/3}\$ %.

Soln.
Ans: a

Let us derive the shortcut formula first, so that you can remember it and use it when the need arises. Suppose the number is 100, and let the increase be x%. The number becomes 100 + x. Let us suppose that it has to be reduced by p% to restore it to 100. Then, (100 + x) - p × \$(100 + x)/100\$ = 100. We can cancel away 100, and easily simplify it to p = \${100 × x}/{100 + x}\$ = \${100 × 100}/{100 + 100}\$ = 50%.

### Question 2

Price of sugar is increased by 60%. By what percentage should consumption be reduced so that the expenditure remains same?

A

\$37{1/2}\$ %.

B

\$38{1/2}\$ %.

C

\$36{1/2}\$ %.

D

\$20{1/4}\$ %.

Soln.
Ans: a

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 60 = Rs. 160/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 160 × c, which gives c = 100/160, so the decrease is 1 - \$100/160\$ = \${160 - 100}/160\$ × 100% = \${75/2}\$, which is same as: \$37{1/2}\$%.

### Question 3

Price of sugar is increased by 80%. By what percentage should consumption be reduced so that the expenditure remains same?

A

\$44{4/9}\$ %.

B

\$51{1/8}\$ %.

C

\$35{6/11}\$ %.

D

\$38{9/11}\$ %.

Soln.
Ans: a

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 80 = Rs. 180/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 180 × c, which gives c = 100/180, so the decrease is 1 - \$100/180\$ = \${180 - 100}/180\$ × 100% = \${400/9}\$, which is same as: \$44{4/9}\$%.

### Question 4

The age of Mr. X is 60% more than Mr. Y's age which is 20 years at present. By what percent is Y's age less than Mr. X's age?

A

\$37{1/2}\$ %.

B

\$38{1/2}\$ %.

C

\$36{1/2}\$ %.

D

\$20{1/4}\$ %.

Soln.
Ans: a

Age of Mr. X is 20 + \${60 × 20}/100\$ = 32 years. Mr. Y's age is less than Mr. X's age by \${60 × 20}/100\$ = 12 years. In terms of percentage, it is \$12/32\$ × 100 = \${75/2}\$, which is same as: \$37{1/2}\$.

### Question 5

In a sample there are 750 items having a value of 50°C. 50% values are below 50°C, and the number of values above 50°C is \$2/3\$ of the items having a value of 50°C. What is the size of the sample?

A

2500 items.

B

2510 items.

C

2490 items.

D

2520 items.

Soln.
Ans: a

The %age ≥ 50°C = (100 - 50) = 50. If x is the size of the sample, 50% of x = 750 + \$2/3 × 750\$ = \${5 × 750}/3\$, which is same as \${50 × x}/100\$ = \${5 × 750}/3\$. Solving, we get x = 2500. 