# Ratio and Proportion Quiz Set 003

### Question 1

A sum of Rs. 9000 is to be divided among three partners, P, Q and R, in the ratio 6 : 5 : 4. What is the difference between the shares of P and Q?

A

Rs. 600.

B

Rs. 602.

C

Rs. 598.

D

Rs. 604.

Soln.
Ans: a

The difference of shares of Q is in the ratio like this: \${6 - 5}/{6 + 5 + 4} × 9000\$ = Rs. 600.

### Question 2

The sides of a triangle are in the ratio 5 : 12 : 9, which is the longest side, if the perimeter is 520?

A

240.

B

242.

C

238.

D

244.

Soln.
Ans: a

Let the sides be 5x, 12x and 9x. We have 5x + 12x + 9x = 520, or 26x = 520, which gives x = 20, so the longest side is 12 × x = 12 × 20 = 240.

### Question 3

Two numbers A and B are in ratio 14 : 15. If they are both increased by 10%, what will be the new ratio of A : B?

A

\${14/15}\$.

B

\$2{1/14}\$.

C

\$2{10/17}\$.

D

\$3{8/17}\$.

Soln.
Ans: a

New A will scale to \$110/100\$ × 14, and B to \$110/100\$ × 15. New ratio is \${110 × 14}/{110 × 15}\$ = \${14/15}\$.

### Question 4

A bag contains 25p, 10p and 5p coins in the ratio 2 : 13 : 12. How many 25 paise coins are there if the total amount is Rs. 48?

A

40.

B

42.

C

38.

D

44.

Soln.
Ans: a

Let the total number of coins be 2x, 13x and 12x. Please note that 25p = Rs. 1/4, 10p = Rs. 1/10, 5p = Rs. 1/20, so they add to x × \$(2/4 + 13/10 + 12/20)\$ = 48. LCM of 4, 10 and 20 is 20, multiplying both sides by 20 we have x × \$(2 × 5 + 13 × 2 + 12)\$ = 48 × 20, which is x × \$(10 + 26 + 12)\$ = 48 × 20, solving for x we get x = 20, so 25p coins = 20 × 2 = 40.

### Question 5

A 400 liter mixture of milk and water contains 86% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

288 liter.

B

289 liter.

C

287 liter.

D

291 liter.

Soln.
Ans: a

The volume of milk will remain same at \${86 × 400}/100\$ = 344 liters. The amount of water at present is 400 - 344 = 56 liters. We need to make the volume of water equal to that of the milk. So we have to add 344 - 56 = 288 liters of water.