type 2 age based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on ratio & proportion topic of quantitative aptitude
(a) 9 years
(b) 15 years
(c) 3 years
(d) 5 years
The correct answers to the above question in:
Answer: (a)
Sonali’s present age
= 5x years
Monali’s present age = 3x years
According to the question,
After 5 years,
${5x + 5}/{3x + 5} =10/7$
${x +1}/{3x + 5} = 2/7$
7x + 7 = 6x + 10
7x - 6x = 10 - 7
x = 3
Monali’s present age
= 3x = 9 years
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Read more age based ratio and proportion problems Based Quantitative Aptitude Questions and Answers
Question : 1
The ratio of the present ages of two boys is 3:4. After 3 years, the ratio of their ages is equal to will be 4:5.The ratio of their ages after 21 years will be
a) 11:12
b) 10:11
c) 17:19
d) 14:17
Answer »Answer: (b)
Let the ages of boys be 3x and 4x years respectively.
According to the question,
After 3 years
${3x + 3}/{4x + 3} = 4/5$
16x + 12 = 15x + 15
16x - 15x = 15 - 12
x = 3
Required ratio after 21 years
= ${3x + 21}/{4x + 21}$
= ${3 ×3 + 21}/{4 × 3 + 21} = {9 + 21}/{12 + 21}$
= $30/33 = 10/11$
Question : 2
Four years ago, the ratio of A’s age to B’s age was 11 : 14 and four years later their age will be in the ratio 13 : 16. The present age of A is
a) 44 years
b) 28 years
c) 26 years
d) 48 years
Answer »Answer: (d)
Let the age of A and B four years ago be 11x and 14x years respectively.
According to the question,
After 4 years from now,
${11x + 8}/{14x + 8} = 13/16$
176x + 128 = 182x + 104
182x - 176x = 128 - 104
6x = 24 ⇒ $x = 24/6$ = 4
A’s present age = (11x + 4) years
= 11 × 4 + 4 = 48 years
Question : 3
The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is :
a) 33 years
b) 30 years
c) 32 years
d) 35 years
Answer »Answer: (d)
A’s present age = 5x years
B’s present age = 6x years
According to the question,
After 7 years,
${5x + 7}/{6x + 7} = 6/7$
36x + 42 = 35x + 49
36x - 35x = 49 - 42
x = 7
A’s present age
= 5x = 35 years
Question : 4
The present age of A and B are in the ratio 4 : 5 and after 5 years they will be in the ratio 5 : 6. The present age of A is
a) 25 years
b) 40 years
c) 20 years
d) 10 years
Answer »Answer: (c)
Let the present age of A and B be 4x and 5x years respectively,
According to the question,
${4x + 5}/{5x + 5} = 5/6$
25x + 25 = 24x + 30
x = 30 - 25 = 5
A’s present age
= 4x = 4 × 5 = 20 years
Question : 5
The sum of the age of a father and his son is 100 years now. 5 years ago their age were in the ratio of 2 : 1. The ratio of the age of father and son after 10 years will be
a) 10 : 7
b) 3 : 5
c) 4 : 3
d) 5 : 3
Answer »Answer: (d)
5 years ago, let the age of father = 2x years (let)
Then, Age of son = x years
2x + 5 + x + 5 = 100
3x = 100 - 10 = 90
$x = 90/3$ = 30
Father’s present age
= 2x + 5 = 60 + 5 = 65 years
Son’s present age = x + 5
= 30 + 5 = 35 years.
After 10 years,
Ratio = ${65 + 10}/{35 + 10}$
$75/45 = 5/3$ = 5 : 3
Question : 6
The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today, is
a) 2 : 3
b) 2 : 5
c) 1 : 3
d) 1 : 2
Answer »Answer: (d)
Let the age of father 10 years hence is 5x years,
then age of son 10 years hence will be 3x years.
According to the question,
${5x - 10 - 10}/{3x - 10 - 10} = 3/1$
${5x - 20}/{3x - 20} = 3/1$
5x - 20 = 9x - 60
4x = 40 or x = 10
Required ratio
= (3x - 10) : (5x - 10)
= 20 : 40 = 1 : 2
GET ratio & proportion PRACTICE TEST EXERCISES
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
ratio & proportion Shortcuts and Techniques with Examples
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