# Ratio and Proportion Quiz Set 017

### Question 1

Two numbers are in the ratio 14 : 13. If both are decreased by 157, the new ratio becomes 109 : 90. What is the first number?

A

266.

B

270.

C

262.

D

274.

Soln.
Ans: a

Let the numbers be 14x and 13x. We are given \${14x - 157}/{13x - 157} = 109/90\$. Solving, we get x = 19, so first number is 19 × 14 = 266.

### Question 2

Mr. X has got a new telephone connection for a plan that has a 30-day rental of Rs. 900. The phone was installed on June 16. What is the amount of the bill for the month of June if billing is done on pro-rata proportionate basis?

A

Rs. 420.

B

Rs. 720.

C

Rs. 1320.

D

Rs. 1020.

Soln.
Ans: a

June has 30 days, so billing is for 30 - 16 = 14 days. The ratio on proportionate basis is \$14/30\$ × 900 = Rs. 420.

### Question 3

Two numbers A and B are in ratio 2 : 3. If they are both increased by 60%, what will be the new ratio of A : B?

A

\${2/3}\$.

B

\$2{1/2}\$.

C

\$2{2/3}\$.

D

\$2{1/5}\$.

Soln.
Ans: a

New A will scale to \$160/100\$ × 2, and B to \$160/100\$ × 3. New ratio is \${160 × 2}/{160 × 3}\$ = \${2/3}\$.

### Question 4

A bag contains 25p, 10p and 5p coins in the ratio 11 : 2 : 8. How many 25 paise coins are there if the total amount is Rs. 67?

A

220.

B

222.

C

218.

D

224.

Soln.
Ans: a

Let the total number of coins be 11x, 2x and 8x. Please note that 25p = Rs. 1/4, 10p = Rs. 1/10, 5p = Rs. 1/20, so they add to x × \$(11/4 + 2/10 + 8/20)\$ = 67. LCM of 4, 10 and 20 is 20, multiplying both sides by 20 we have x × \$(11 × 5 + 2 × 2 + 8)\$ = 67 × 20, which is x × \$(55 + 4 + 8)\$ = 67 × 20, solving for x we get x = 20, so 25p coins = 20 × 11 = 220.

### Question 5

If \$2/9\$ of A's amount is \$4/12\$ of B's amount, and the total amount they have is Rs. 2500, what is the amount with A?

A

Rs. 1500.

B

Rs. 1502.

C

Rs. 1498.

D

Rs. 1504.

Soln.
Ans: a

Let the amounts with them be A and B. So \$2/9\$A = \$4/12\$B, which can be re-arranged to get A : B = 3 : 2. So A = \$3/5 × 2500\$ = Rs. 1500. 