Ratio Questions and Answers - Practice Problems & Solutions

Q11 :

Divide Rs. 2430 among three persons A, B and C so that if their shares be diminished by Rs. 5, Rs. 10, Rs. 15 respectively, the remainder shall be in the ratio of 3:4:5.

A

1015, 810, 605

B

605, 1015, 810

C

605, 1000, 825

D

605, 810, 1015

View Answer

Correct Answer: D

605, 810, 1015

Description:

Divide [Rs. 2430 - (5 + 10+ 15)] in the ratio 3 : 4 : 5 and thereafter and 5, 10 and 15 to their result.

Q12 :

If 1 gm of gold 10 carats of fine, 1 gm of gold 11 carats of fine, 2 gm of gold 12 carats of fine, and 5 gm of gold 13 carats of fine be mixed together, find the fineness of the resulting compound.

A

12

B

15

C

12.5

D

$12frac{2}{9}$

View Answer

Correct Answer: D

$12frac{2}{9}$

Description:

$= frac{1 times 10 + 1 times 11 + 2 times 12 + 5 times 13}{1 + 1 + 2 + 5} = 12 frac{2}{9}$

Q13 :

Divide 37 into two parts so that 5 times one part and 11 times the other are together 227.

A

20, 17

B

25, 12

C

15, 22

D

30, 7

View Answer

Correct Answer: D

30, 7

Description:

$5x + 11(37 - x) = 227$

$therefore x = 30 text{ and the other part is } 7$

Q14 :

Annual income of A and B is in the ratio of 4 : 3 and this annual expenses bear a ratio of 3 : 2. If each of them saves Rs. 600 at the end of the year, the annual income of A is

A

Rs. 4800

B

Rs. 1800

C

Rs. 1200

D

Rs. 2400

View Answer

Correct Answer: D

Rs. 2400

Description:

Let the income of A be Rs. 2400, so that income of B is

$frac{3}{4} times 2400 = 1800$

Since each saves Rs. 600, the ratio of their saving is 3 : 2. Hence this is the correct choice.

Q15 :

In a bag there are coins of 50 paise, 25 paise and one rupee in the ratio of 5 : 6 : 2. If there are in all Rs. 42. The number of 25 paise coins is

A

40

B

42

C

44

D

46

View Answer

Correct Answer: B

42

Description:

Total value of one group of 5 coins of 50 P,
6 coins of 25 P and
2 coins of one rupee = Rs. 2.50 + Rs. 1.50 + Rs. 2.00 = Rs. 6.00

Since the total value is Rs. 42; So there are 7 such groups.

The number of 25 P coins = 7 $times$ 6 = 42

Q16 :

Two numbers are in the ratio 3 : 7 and if 6 be added to each of them, they are 5 : 9, then the numbers are

A

6, 14

B

15, 35

C

9, 21

D

39, 91

View Answer

Correct Answer: C

9, 21

Description:

Check from choice

$9 : 12 Rightarrow 3 : 7 text{ true}$

$(9 + 6) : (21 + 6) = 15 : 27 Rightarrow 5 : 9 text{ true}$

Q17 :

A man wishes to divide his monthly savings of Rs. 846 between his two sons and one daughter in the ratio $frac{1}{4} : frac{1}{5} : frac{1}{3}$ respectively. How much should he give to his daughter?

A

Rs. 300

B

Rs. 270

C

Rs. 216

D

Rs. 360

View Answer

Correct Answer: D

Rs. 360

Description:

$= frac{1}{4} : frac{1}{5} : frac{1}{3} = 15 : 12 : 20$

(L.C.M. of 4, 5, 3 = 60)

Daughter's share = $= frac{20}{47} times text{ Rs. } 846 = text{ Rs. } 360$

Q18 :

In a school, the ratio of the number of teachers to the number of student is 3 : 25. If the total number of students and teachers in the school is 896, then the number of teachers in the school is

A

32

B

64

C

90

D

96

View Answer

Correct Answer: D

96

Description:

Number of teachers $= frac{3}{28} times 896 = 96$

Q19 :

If 10% of $x$ is equal to 20% of $y$ , then $x:y$ is equal to

A

1:2

B

2:1

C

5:1

D

10:1

View Answer

Correct Answer: B

2:1

Description:

$= frac{10}{100} x = frac{20}{100}y Rightarrow frac{x}{y} = frac{2}{1}$

Q20 :

A drum contains 20 litres of a paint. From this, 2 litres of paint is taken out and replaced by 2 litres of paint is taken out and replaced by 2 litres of oil. Again 2 litres of this mixture is taken out and replaced by 2 litres of oil. If this operation is performed once again, then the final ratio of paint and oil in the drum would be:

A

729 : 271

B

172 : 279

C

3 : 7

D

217 : 972

View Answer

Correct Answer: A

729 : 271

Description:

$begin{aligned} text{After 1st operation, paint} &= 18text{L} text{oil } &= 2text{L} text{ After 2nd operation, paint} &= 18 - frac{18}{20} times 2 &= 16.2text{L} text{oil } &= 2 - frac{2}{10} + 2 = 3.8text{L} text{After 3rd operation, paint } &=16.2 - frac{16.2}{20} times 2 = 14.58text{L} text{oil } &= 3.8 - frac{3.8}{10} times 2 + 2 = 5.42text{L} text{Ratio } &= frac{14.58}{5.42} = frac{729}{271} end{aligned}$