Wednesday, 3 February 2016

MATHS (SOLVED IN STEPS) Problems on Age - (Page -1)

MATHS (SOLVED IN STEPS)
Problems on Age - (Page -1)
1. A man's age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?
A.70   B.60    C.50       D.40
Answer : Option C
Explanation :
Let the age before 10 years = x
       Then 125x/100 = x + 10
       =>125x = 100x + 1000
       => x = 1000/25 = 40
Present age = x + 10 = 40 +10 = 50

2. Ten years ago, R was half of S in age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
A. 45  B. 40  C. 35   D. 30
Answer : Option C
Explanation :Let the present age of R and S be 3x and 4x respectively. Ten years ago, R was half of S in age
=> (3x – 10) = ½ (4x – 10)
         => 6x – 20 = 4x – 10
         => 2x = 10
         => x = 5
total of their present ages = 3x + 4x = 7x = 7 × 5 = 35

3. Father is aged three times more than his son Anil. After 8 years, he would be two and a half times of Anil's age. After further    8 years, how many times would he be of Anil's age?
A. 4 times    B. 5 times   C. 2 times  D. 3 times
Answer : Option C
Explanation :
Assume that Anil's present age = x.
Then father's present age = 3x + x = 4x
After 8 years, fathers age = 2 ½ times of Anils' age
=> (4x+8) = 2 ½ × (x+8)
=> 4x + 8 = (5/2) ×(x + 8)
 => 8x + 16 = 5x+ 40
 => 3x = 40-16 = 24
 => x = 24/3 = 8
After further 8 years,
Anil's age = x + 8+ 8 = 8+8+8 = 24
Father's age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48
Father's age/Anil's age = 48/24 = 2

4. A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
A.23      B.22      C.21    D.20
Answer : Option B
Explanation :
Let the present age of the son = x years
Then present age the man = (x+24) years
Given that in 2 years, man's age will be twice the age of his son
=> (x+24) +2 = 2(x+2)
=> x = 22

5. Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years?
A.28    B.27    C.26   D.24
Answer : Option D
Explanation :
Ratio of the present age of Kiran and Syam = 5 : 4
=> Let the present age of Kiran = 5x
Present age of Syam = 4x
After 3 years, ratio of their ages = 11:9
=> (5x + 3) : (4x + 3) = 11 : 9
=> (5x+3) / (4x+3) = 11/9
=> 9(5x + 3) = 11(4x + 3)
=> 45x + 27 = 44x + 33
=> x = 33-27 =6
Syam's present age = 4x = 4×6 = 24

6. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?
A. 6    B.5    C.4    D.3
Answer : Option C
Explanation :
Let the age of the youngest child = x
Then the ages of 5 children can be written as x,
(x+3), (x+6),(x+9) and (x+12)
X + (x+3) + (x+6) + (x+9) + (x+12) = 50
=> 5x + 30 =50
=> 5x = 20
=> x = 20/5 = 4

7. A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B?
A.10       B.9   C.8  D.7
Answer : Option A
Explanation :
Let the age of C = x. Then
Age of B = 2x
Age of A = 2 + 2x
The total age of A,B and C =27
=> (2+2x) + 2x + x = 27
=> 5x = 25
=> 25/5 = 5
B's age = 2x = 2×5 = 10

8. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
A. 48    B. 45   C. 43       D. 44
Answer : Option D
Explanation :
Total age of all students = 22×21

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