# Ratio and Proportion Quiz Set 005

### Question 1

The ratio of shares of three friends in Rs. 2700 are in an A.P.(arithmtic progression). What is the share of the friend who is neither the richest, nor the poorest?

A

Rs. 900.

B

Rs. 904.

C

Rs. 896.

D

Rs. 908.

Soln.
Ans: a

Let the shares be in the ratio a - d : a : a + d. The value of the middle item is \$a/{(a - d) + a + (a + d)}\$ × 2700 = \$a/{3a}\$ × 2700 = \$2700/3\$ = Rs. 900.

### Question 2

Two numbers are in the ratio 5 : 12. If both are decreased by 49, the new ratio becomes 16 : 107. What is the first number?

A

65.

B

69.

C

61.

D

73.

Soln.
Ans: a

Let the numbers be 5x and 12x. We are given \${5x - 49}/{12x - 49} = 16/107\$. Solving, we get x = 13, so first number is 13 × 5 = 65.

### Question 3

A bag contains 25p, 10p and 5p coins in the ratio 12 : 14 : 3. How many 25 paise coins are there if the total amount is Rs. 91?

A

240.

B

242.

C

238.

D

244.

Soln.
Ans: a

Let the total number of coins be 12x, 14x and 3x. Please note that 25p = Rs. 1/4, 10p = Rs. 1/10, 5p = Rs. 1/20, so they add to x × \$(12/4 + 14/10 + 3/20)\$ = 91. LCM of 4, 10 and 20 is 20, multiplying both sides by 20 we have x × \$(12 × 5 + 14 × 2 + 3)\$ = 91 × 20, which is x × \$(60 + 28 + 3)\$ = 91 × 20, solving for x we get x = 20, so 25p coins = 20 × 12 = 240.

### Question 4

Two numbers are in the ratio 19 : 9. If both are increased by 18, the new ratio becomes 52 : 27. What is the first number?

A

190.

B

194.

C

186.

D

198.

Soln.
Ans: a

Let the numbers be 19x and 9x. We are given \${19x + 18}/{9x + 18} = 52/27\$. Solving, we get x = 10, so first number is 10 × 19 = 190.

### Question 5

A 350 liter mixture of milk and water contains 62% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

84 liter.

B

85 liter.

C

83 liter.

D

87 liter.

Soln.
Ans: a

The volume of milk will remain same at \${62 × 350}/100\$ = 217 liters. The amount of water at present is 350 - 217 = 133 liters. We need to make the volume of water equal to that of the milk. So we have to add 217 - 133 = 84 liters of water. 