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Ratio and Proportion

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 ?
A
40 years
B
28 years
C
32 years
D
36 years
Arithmetic Aptitude 3    Ratio and Proportion    Age    
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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?
A
32
B
40
C
30
D
36
Arithmetic Aptitude 3    Ratio and Proportion    Age    
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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
A
15,20,35
B
20,24,36
C
20,25,45
D
16,20,36
Arithmetic Aptitude 3    Ratio and Proportion    Age    
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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 = 4
Present 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:
A
6, 27
B
8, 36
C
38, 171
D
20, 90
Arithmetic Aptitude 4    HCF    Ratio and Proportion    
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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?
A
200, 360, 160
B
135, 250, 150
C
90, 60, 110
D
Cannot be determined
Ratio and Proportion    
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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:
A
8:16:15
B
23:33:60
C
33:30:20
D
21:25:32
Ratio and Proportion    
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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:
A
3:9:5
B
7:5:3
C
2:3:4
D
2:5:4
Ratio and Proportion    
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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:
A
7:3
B
5:6
C
2:3
D
None of these
Ratio and Proportion    
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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.
A
15 years
B
10 years
C
7 years
D
18 years
Ratio and Proportion    
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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.
A
69.4 km/h
B
78.6 km/h
C
87.5 km/h
D
40.5 km/h
Ratio and Proportion    Time Speed Distance    
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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.
There are 14 questions to complete.
12

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