## Ratio and Proportion

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Question 1 |

Present age of Vinod and Ashok are in ratio of 3:4 respectively. After 5 years, the ratio of their ages becomes 7:9 respectively. What is Ashok’s present age is ?

40 years | |

28 years | |

32 years | |

36 years |

**Arithmetic Aptitude 3**

**Ratio and Proportion**

**Age**

**Discuss it**

Question 1 Explanation:

Let the present age of Vinod and Ashok be 3x years and 4x years respectively.

Then (3x+5) / (4x+5) = 7 / 9 ∴ 9(3x + 5) = 7(4x + 5) ∴ 27x + 45 = 28x + 35 ∴ x = 10 ∴ Ashok’s present age = 4x = 40 years

Question 2 |

At present, the ratio between ages of Ram and Shyam is 6:5 respectively. After 7 years, Shyam’s age will be 32 years. What is the present age of Ram?

32 | |

40 | |

30 | |

36 |

**Arithmetic Aptitude 3**

**Ratio and Proportion**

**Age**

**Discuss it**

Question 2 Explanation:

Let the present age of Ram and Shyam be 6x years and 5x years respectively. Then 5x + 7 = 32 ∴ 5x = 25 ∴ x = 5 ∴ Present age of Ram = 6x = 30 years

Question 3 |

The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum of their ages was 45 years. Find their present ages in years

15,20,35 | |

20,24,36 | |

20,25,45 | |

16,20,36 |

**Arithmetic Aptitude 3**

**Ratio and Proportion**

**Age**

**Discuss it**

Question 3 Explanation:

Let the current ages of A, B and C be ax years, 5x years and 9x respectively.

Then (4x-9) + (5x-9) + (9x-9) =45 ∴ 18x – 27 = 45 ∴ 18x = 72 ∴ x = 4Present ages of A, B and C are 4x = 16, 5x = 20, 9x = 36 respectively.

Question 4 |

Two numbers are in the ratio of 2:9. If their H. C. F. is 19, numbers are:

6, 27 | |

8, 36 | |

38, 171 | |

20, 90 |

**Arithmetic Aptitude 4**

**HCF**

**Ratio and Proportion**

**Discuss it**

Question 4 Explanation:

Let the numbers be 2X and 9X Then their H.C.F. is X, so X = 19 ∴ Numbers are (2x19 and 9x19) i.e. 38 and 171

Question 5 |

In a box, there are 10p, 25p and 50p coins in the ratio 4:9:5 with the total sum of Rs 206. How many coins of each kind does the box have?

200, 360, 160 | |

135, 250, 150 | |

90, 60, 110 | |

Cannot be determined |

**Ratio and Proportion**

**Discuss it**

Question 5 Explanation:

Let the number of 10p, 25p, 50p coins be 4x, 9x, 5x respectively. Then,
4x/10 + 9x/4 + 5x/2 = 206 (Since, 10p = Rs 0.1, 25p = Rs 0.25, 50p = Rs 0.5)
=> 8x + 45x + 50x = 4120 (Multiplying both sides by 20 which is the LCM of 10, 4, 2)
=> 103x = 4120
=> x = 40.
Therefore,
No. of 10p coins = 4 x 40 = 160 (= Rs 16)
No. of 25p coins = 9 x 40 = 360 (= Rs 90)
No. of 50p coins = 5 x 40 = 200 (= Rs 100)

Question 6 |

Mark, Steve and Bill get their salaries in the ratio of 2:3:5. If their salaries are incremented by 15%, 10%, and 20% respectively, the new ratio of their salaries becomes:

8:16:15 | |

23:33:60 | |

33:30:20 | |

21:25:32 |

**Ratio and Proportion**

**Discuss it**

Question 6 Explanation:

Let their old salaries be 2a, 3a, 5a respectively. Then, their new salaries become:
115% of 2a = 2a x 1.15 = 2.3a
110% of 3a = 3a x 1.10 = 3.3a
120% of 5a = 5a x 1.20 = 6a
So, the new ratio becomes
2.3a:3.3a:6a
Upon simplification, this becomes
23:33:60

Question 7 |

In a library, the ratio of the books on Computer, Physics and Mathematics is 5:7:8. If the collection of books is increased respectively by 40%, 50% and 75%, find out the new ratio:

3:9:5 | |

7:5:3 | |

2:3:4 | |

2:5:4 |

**Ratio and Proportion**

**Discuss it**

Question 7 Explanation:

40% increase will lead to a factor of 140 and similiarly 150 and 175
so new ratio is
(5*140):(7*150):(8*175)
on solving we get 2:3:4

Question 8 |

The ratio 5:3 represents 16 liters of a mixture containing milk and water. If 4 liters of water is added and 4 liters of milk is extracted from the mixture, then the ratio of the mixture will be:

7:3 | |

5:6 | |

2:3 | |

None of these |

**Ratio and Proportion**

**Discuss it**

Question 8 Explanation:

Amount of Milk in 16 litres of mixture: (5/8) x 16 = 10 litres
Amount of Water in 16 litres of mixture: 16-10 = 6 litres
If we add 4 litres of water and extract 4 litres of milk, the total volume remains the same.
Amount of Milk in 16 litres of new mixture: = 10 - 4 = 6 litres
Amount of Water in 16 litres of new mixture: = 6 + 4 = 10 litres
So, the new ratio becomes 3:5.

Question 9 |

If the ages of Jacob, Max and Samuel are in the proportion 3:5:7 and the average of their ages is 25 years, then find the age of the youngest person.

15 years | |

10 years | |

7 years | |

18 years |

**Ratio and Proportion**

**Discuss it**

Question 9 Explanation:

Let their ages be 3a, 5a and 7a. Then,
(3a + 5a + 7a) / 3 = 25
=> 15a/3 = 25
=> 5a = 25
=> a = 5
Therefore, age of the youngest person = 3a = 15 years

Question 10 |

The ratio of the speed of two trains is 7:8. If the second train covers 400 km in 4 h, find out the speed of the first train.

69.4 km/h | |

78.6 km/h | |

87.5 km/h | |

40.5 km/h |

**Ratio and Proportion**

**Time Speed Distance**

**Discuss it**

Question 10 Explanation:

Let the speed of the two trains be 7x and 8x.
Then, 8x = 400 / 4
⇒ 8x = 100 ⇒ x = 12.5 km/h.
Hence, speed of the first train = 7x = 7 × 12.5 = 87.5 km/h.

Question 11 |

A certain amount of money is distributed between Alfred, Adam, Harry and Leo in the proportion of 5:2:4:3. Harry's share is Rs 1000 more than Leo's share. How much money does Adam get?

Rs 800 | |

Rs 1000 | |

Rs 1050 | |

Rs 2000 |

**Ratio and Proportion**

**Discuss it**

Question 11 Explanation:

Let the shares of Alfred, Adam, Harry and Leo be Rs 5x, Rs 2x, Rs 4x and Rs 3x respectively. Then,
4x - 3x = 1000 ⇒ x = 1000.
Therefore, Adam gets = Rs 2x = Rs 2000.

Question 12 |

If (x:y) = 2:1, then (x²-y²):(x²+y²) = __ ?

1:2 | |

3:5 | |

2:1 | |

5:4 |

**Ratio and Proportion**

**Discuss it**

Question 12 Explanation:

Given, x:y = 2:1 ⇒ x²:y² = 4:1.
Then, (x²+y²):(x²-y²) = (4+1)/(4-1) [by applying Componendo & Dividendo].
⇒ (x²-y²):(x²+y²) = 3/5.

Question 13 |

Syrup and Water are mixed in 2:1 ratio to form 60 litres of a mixture. How much water needs to be added to make the ratio 1:2?

60 litres | |

85 litres | |

55 litres | |

Cannot be determined |

**Ratio and Proportion**

**Discuss it**

Question 13 Explanation:

Volume of Syrup in the mixture = 60 × 2/3 = 40 litres.
Volume of Water in the mixture = 60 × 1/3 = 20 litres
Let the required volume of water be x litres. Then,
40:(20+x) = 1:2
⇒ 20+x = 80
⇒ x = 60 litres.

Question 14 |

Felix and Adam win Rs 1210 together. 4/15 of Felix's share is same as 2/5 of Adam's share. How much did Adam win?

Rs 484 | |

Rs 330 | |

Rs 360 | |

Data inadequate |

**Ratio and Proportion**

**Discuss it**

Question 14 Explanation:

Let Felix's and Adam's share be F and A respectively. Then,
4/15 × F = 2/5 × A
⇒ 20 F = 30 A
⇒ F/A = 3/2
⇒ F:A = 3:2.
Therefore, Adam won = 2/5 of Rs 1210 = Rs 484.

There are 14 questions to complete.