# Percentages Quiz Set 019

### Question 1

A shopkeeper sells 59% items of his stock and still has 656 items left with him. How many items did he have at the beginning?

A

1600 items.

B

1700 items.

C

1500 items.

D

1800 items.

Soln.
Ans: a

Let the items be x. His % stock left is 100 - 59 = 41, so 41% of x = 656, which gives x = \$656/41\$ × 100 = 1600 items.

### Question 2

In a sample there are 450 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

1500 items.

B

1510 items.

C

1490 items.

D

1520 items.

Soln.
Ans: a

The %age ≥ 50°C = (100 - 50) = 50. If x is the size of the sample, 50% of x = 450 + \$2/3 × 450\$ = \${5 × 450}/3\$, which is same as \${50 × x}/100\$ = \${5 × 450}/3\$. Solving, we get x = 1500.

### Question 3

A bag contains 630 red, 1020 green and 1350 blue marbles. What percentage of the total is the most visible color in the bag?

A

45 %.

B

55 %.

C

35 %.

D

65 %.

Soln.
Ans: a

By inspection, blue is the most visible color. The percentage of blue is \$1350/{630 + 1020 + 1350}\$ × 100 = 45%.

### Question 4

Two numbers are, respectively, 5% and 35% less than a third number. What percent is the second of the first?

A

\$68{8/19}\$ %.

B

\$73{5/18}\$ %.

C

61 %.

D

\$64{13/21}\$ %.

Soln.
Ans: a

If the third number is 100, first number is (100 - 5) = 95, and the second number is (100 - 35) = 65. The required ratio is \$65/95\$ × 100 = \${1300/19}\$, which is same as: \$68{8/19}\$%.

### Question 5

If 4% of A + B = 9% of A - B, then what percent of B is A?

A

\$2{3/5}\$ %.

B

\$4{1/2}\$ %.

C

\$1{1/7}\$ %.

D

4 %.

Soln.
Ans: a

We have been given 4% of A + B = 9% of A - B, so \${A + B}/{A - B}\$ = \$9/4\$. By componendo and dividendo, \${(A + B) + (A - B)}/{(A + B) - (A - B)}\$ = \${9 + 4}/{9 - 4}\$, which gives \$A/B\$ = \$13/5\$ = \${13/5}\$, which is same as: \$2{3/5}\$% 