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Home » Aptitude » Ratio & Proportion » Page 3

The ages of raju amd biju are in the ratio 3:1 fifteen years hence,the ratio will be 2:1 their present ages are

A.

10

B.

15

C.

21

D.

20

Answer with explanation

Answer: Option BExplanation

The ratio of ages ,

=> 3:1

Let the age of raju be 3x .

And age of biju be x.

From the question,

=> x=15.

So, The age of raju is 3×15 =45years.

The age of biju=> 15.

Workspace

In a school, 10% of the boys are same in number as (1/4)th of the girls. what is the ratio of boys to girls in the school?

A.

3 : 2

B.

5 : 2

C.

2 : 1

D.

4 : 3

Answer with explanation

Answer: Option BExplanation

Let the number of boys in school be b

Let the number of girls in school be g.

Therefore , According to Question , 10% of boys is equal to 1/4 of girls→

10b/100 = 1g/4

or, 4×10b = 100×g

or, 40b = 100g

or, b/g = 100/40

or, b:g = 5:2

Workspace

If 2A = 3B = 4C, find A : B : C

A.

6 : 5: 3

B.

2 : 4 : 3

C.

6 : 4 : 8

D.

6 : 4 : 3

Answer with explanation

Answer: Option DExplanation

Let 2A = 3B = 4C = x

So, A = x/2 B = x/3 C = x/4

The L.C.M of 2, 3 and 4 is 12

Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12

= 6x : 4x : 3x

= 6 : 4 : 3

Therefore, A : B : C = 6 : 4 : 3

Workspace

Divide $370 into three parts such that second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Find each part.

A.

500

B.

700

C.

400

D.

200

Answer with explanation

Answer: Option DExplanation

Let the first and the third parts be 3x and 5x.

Second part = 1/4 of third part.

= (1/4) × 5x

= 5x/4

Therefore, 3x + (5x/4) + 5x = 370

(12x + 5x + 20x)/4 = 370

37x/4 = 370

x = (370 × 4)/37

x = 10 × 4

x = 40

Therefore, first part = 3x

= 3 × 40

= $120

Second part = 5x/4

= 5 × 40/4

= $50

Third part = 5x

= 5 × 40

= $ 200

Workspace

Find the third proportional of 16 and 20.

A.

25

B.

28

C.

27

D.

25

Answer with explanation

Answer: Option DExplanation

Let the third proportional of 16 and 20 be x.

Then 16, 20, x are in proportion.

This means 16 : 20 = 20 : x

So, 16 × x = 20 × 20

x = (20 × 20)/16 = 25

Therefore, the third proportional of 16 and 20 is 25.

Workspace

In a mixture of 13 litres, the ratio of milk and water is 3 : 2. If 3 liters of this mixture is replaced by 3 liters of milk, then what will be the ratio of milk and water in the newly formed mixture?

A.

10 : 3

B.

8 : 5

C.

1 : 1

D.

1 : 1

Answer with explanation

Answer: Option CExplanation

Total quantity of mixture = 13 liters

3 litres of mixture is removed from the container – So, let’s forget this altogether!

Now, you are left with only 10 litres of mixture in 3:2 ratio.

Milk in 10 litres mix = 10 x | 3 | = 6 litres |

(2 + 3) |

Water in 10 litres mix = 10 x | 2 | = 4 litres |

(2 + 3) |

We add 3 litres milk to this.

So, milk in new mix is = 6 liters + 3 litres = 9 litres

Water= 4 litres

Ratio of milk : water = 9 : 4

Workspace

A.

Rs. 15

B.

Rs. 12

C.

Rs. 10

D.

Rs. 9

Answer with explanation

Answer: Option DExplanation

Assume that the daily wages of man, women and daughter are Rs 5x, Rs. 4x, Rs 3x respectively.

Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.

[3 x (5x)] + [2 x (4x)] + [4 x (3x)] = 105

[15x + 8x + 12x] = 105

35x = 105

x = 3

Hence, man’s daily wage = 5x = 5 x 3 = Rs. 15

Wife’s daily wage = 4x = 4 x 3 = Rs. 12

Daughter’s daily wage = 3x = 3 x 3 = Rs. 9

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A purse contains 342 coins consisting of one rupees, 50 paise and 25 paise coins. If their values are in the ratio of 11 : 9 : 5 then find the number of 50 paise coins?

A.

180

B.

150

C.

162

D.

99

Answer with explanation

Answer: Option CExplanation

Let the value of one rupee, 50 paise and 25 paise be 11x, 9x, 5x respectively.

No. of 1 rupee coins = (11x / 1) =11x

No. of 50 paise coins = (9x / 0.5) = 18x

No. of 25 paise coins = (5x / 0.25) = 20x

11x + 18x + 9x = 342

38x = 342

x = 9

Therefore, no. of 1 rupee coins = 11 x 9 = 99 coins

No. of 50 paise coins = 18 x 9 = 162 coins

No. of 25 paise coins = 20 x 9 = 180 coins

Workspace

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A.

20:21:22

B.

25:24:26

C.

23 : 33 : 60

D.

26:25:24

Answer with explanation

Answer: Option CExplanation

Let salary of

A = 2k,

B = 3k,

C = 5k

=>A’s new salary = 115/100 of 2k = 115/100 x 2k = 23k/13

=>B’s new salary = 110/100 of 3k = 110/100 x 3k = 33k/10

=>C’s new salary = 120/100 of 5k = 120/100 x 5k = 6k

Hence,new ratio = 23k/13 : 33k/10 : 6k = 23 : 33 : 60

Workspace

A mixture contains milk and water in the ratio of 5:1. Adding 5 L of water changes the ratio to 5:2. What was the quantity of milk in the original mixture?

A.

16 litres

B.

25 litres

C.

24 litres

D.

22.75 litres

Answer with explanation

Answer: Option BExplanation

Milk:Water (Initial Ratio) = 5:1 i.e. 5 parts of milk out of 6 (5 + 1) parts of the mixture

Milk:Water (Final Ratio) = 5:2 i.e. 5 parts of milk out of 7 (5 + 2) parts of the mixMilkture

On comparing, 1 part of the mixture has been added (5 litres of water is added). So, 1 part of the mixture = 5 litres

Quantity of milk in the original mixture = 5 parts i.e. 5*5 = 25 litres

Workspace

Divide 680 so that a gets two third of B B gets one fourth of C share

A.

Rs. 480

B.

Rs. 360

C.

Rs. 80

D.

Rs. 300

Answer with explanation

Answer: Option CExplanation

Let the share of c be X

then b gets 1/4 of c

so

B = X/4

& a gets two third of B

then

A = 2/3*X/4 = X/6

Now

=> X +X/4 +X/6 = 680

=> take LCM

=>( 12x+3x+2x)/12 = 680

=> 17x = 680×12

=> X = 680*12/15

=> X = 40*12

=> X = 480

so

c got = 480Rs

B got = 480/4 = 120 Rs

A got = 480/6 = 80 Rs

Workspace

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

A.

50

B.

100

C.

150

D.

200

Answer with explanation

Answer: Option CExplanation

Let the number of 25 p, 10 p and 5 p coins be *x*, 2*x*, 3*x* respectively.

Then, sum of their values = Rs. | 25x |
+ | 10 x 2x |
+ | 5 x 3x |
= Rs. | 60x |
||

100 | 100 | 100 | 100 |

60x |
= 30 | x = |
30 x 100 | = 50. | |

100 | 60 |

Hence, the number of 5 p coins = (3 x 50) = 150.

Workspace

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A.

20

B.

30

C.

48

D.

58

Answer with explanation

Answer: Option BExplanation

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = | 5 x | 3 | : | 8 x | 3 | = 3 : | 24 | ||||

5 | 5 | 5 |

A : B : C = 2 : 3 : | 24 | = 10 : 15 : 24 |

5 |

B = | 98 x | 15 | = 30. |

Workspace

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:

A.

20 litres

B.

30 litres

C.

40 litres

D.

60 litres

Answer with explanation

Answer: Option DExplanation

Quantity of milk = | 60 x | 2 | litres = 40 litres. | |

3 |

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be *x* litres.

Then, milk : water = | 40 | . | ||

20 + x |

Now, | 40 | = | 1 | ||

20 + x |
2 |

20 + *x* = 80

*x* = 60.

Quantity of water to be added = 60 litres.

Workspace

A, B and C have amounts in the ratio of 3 : 4 : 5. First B gives 1/4th to A and 1/4th to C then C gives 1/6th to A. Find the final ratio of amount of A, B and C respectively.

A.

4:3:5

B.

5:4:3

C.

3:4:5

D.

5:2:5

Answer with explanation

Answer: Option DExplanation

A B C

3x 4x 5x

(3x+x) 2x (5x+x) (B Gives 1/4 to A and 1/4 to C)

=4x 2x 6x

(4x+x) 2x 5x ( C Gives 1/6 to A)

=5x 2x 5x

Therefore, 5 : 2 : 5

Workspace

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