# Percentages Quiz Set 003

### Question 1

One number is 120 more than the other, and it is 65% of the sum of them. What is the number?

A

260.

B

360.

C

160.

D

460.

Soln.
Ans: a

Let the numbers be x and x - 120. We have been given x = \$65/100\$ × (x + x - 120), which gives 100x = 65 × (2x - 120), solving, we get x = 260.

### Question 2

A number is first increased by 40%, and thereafter it is reduced by 40% again. What is the overall reduction?

A

16 %.

B

18 %.

C

14 %.

D

20 %.

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. When it is reduced by x%, we get 100 + x - \$((100 + x) × x)/100\$ = 100 + x - \$(x + x^2/100)\$ = 100 - \$x^2/100\$, hence a reduction of \$x^2/100\$ = 16%

### Question 3

A shopkeeper sells 75% items of his stock and still has 200 items left with him. How many items did he have at the beginning?

A

800 items.

B

900 items.

C

700 items.

D

1000 items.

Soln.
Ans: a

Let the items be x. His % stock left is 100 - 75 = 25, so 25% of x = 200, which gives x = \$200/25\$ × 100 = 800 items.

### Question 4

The service tax is 5%. A person receives a telephone bill amounting to Rs. 525. How much was the bill excluding tax?

A

Rs. 500.

B

Rs. 510.

C

Rs. 490.

D

Rs. 520.

Soln.
Ans: a

Let the calls be for Rs. x. The total bill is x + 5% of x = \${21x}/20 = 525\$, which gives x = Rs. 500.

### Question 5

The sum of two numbers is 1712. One of them is 114% of the other. The smaller number is?

A

800.

B

810.

C

790.

D

820.

Soln.
Ans: a

Let the numbers be x and \${114x}/100\$. The sum is x + \${114x}/100\$ which is same as \${214x}/100 = 1712\$. Solving we get the smaller number x = 800. 