Friday, 11 March 2016

Aptitude Questions with Answers : Problems on Ages


To solve problems on ages, student should have knowledge of rations and linear equations. Here problems usually involve comparison of ages in the present, several years ago or several years from now.
Linear Equation:
An equation involving only one unknown variable is a linear equation.

Problems on Ages.
Aptitude Questions with Answers – Problem on Ages  1
The present ages of A,B and C are in the ratio of 5:7:8. Seven years ago, the sum of their ages was 59.What is the present age of eldest one?
a)20 years     b)28 years      c)32 years        d)40 years
Answer :C
Explanation: Let their present ages be 5x, 7x and 8x.
 7 years ago, sum of their ages was 59.
Sum of their present ages = 59 +( 3 x 7) = 80
Sum of their present ages given is 5x + 7x + 8x = 20x 
    20x = 80 =>x =
80 / 20
=4
Age of the Eldest one= 8x = 8x 4 = 32 years.

Word Problems for GMAT – Age related problems 2
In Ravindra Bharathi School, there are 80 boys of age 14 each, 70 boys of age 15 each and 50 boys of age 13 each and another 60 boys of age 12 each. The average age of the boys of the school is
     a)    13.6 years    b)12.5 years     c)13 years     d)14.2 years
Answer: A
Explanation: 
Average age of boys = Sum of the ages of all boys/ Total number of boys
                              =
(80 x14)+(70x15)+(50x13)+(60x12) / (80+70+50+60)
          =
(1120+1050+650+720) / 260
                               =3540/260 =13.6

Aptitude questions with explanations : Problems on Ages 3
Three years ago, the average age of P and Q was 20 years. With R joining them, their average age becomes 23 years. What is the age of R?
a)18 years      b)20 years     c)23 years      d)25 years
Answer :C
Explanation:  Three years ago, the average age of P and Q was 20 years.
           Three years ago, their sum of the ages was 2x20= 40 years
            Present age of P+Q+R  = 3 X23 =69
              Present age of P+Q=40+( 2 x 3)= 46
Present age of R = ( P+Q+R)- (P+Q)=  69-46 =23 years

Arithmetic study material – Age related problems 4
 The average age of 4 boys is 14 years. Their ages are in the ratio of 3:5:4:2. Find the age of the youngest boy ?
a) 8 years      b)6 years      c)12 years    d)14 years
Answer :A
Explanation :
Sum of the ages of 4 boys = Average x Number of Boys = 4x 14 = 56
    Age of the youngest boy = 56 x
2 / 14
= 8 years

Quantitative aptitude for CAT – Problems on Ages 5
The ratio between the ages of Shastri and Varma is 5:6 and sum of their ages is 55 years. What is the ratio of their ages after 5 years ?
a) 3:4        b)4:5            c)5:6         d)6:7
Answer:D
Explanation:  Present age of Shastri= 55 x
5 / 11
= 25 years
               Present age of Varma = 55 x
6 / 11
= 30 years
After 5 years, age of shastri will be   = 25 +5 = 30 years   , Age of Varma will be = 30+5 =35  years
Ratio of their ages after 5 years will be = 30: 35 = 6 :7

Aptitude questions and word problems – Ages 6
6. The ratio between the present age of Sudheer and Sravani is 7:8. If Sravani is 5 years older than Sudheer, what will be the ratio of their ages after 9 years ?
a) 8:9       b)9:10        c)5:7            d)6:4
Answer:
Explanation : Let present age of Sudheer and Sravani be 7x and 8x years respectively.
Sravani is 5 years older than Sudheer, means the difference between their ages is 5 years
    Difference of ages = 8x- 7x = x = 5 years
Present age of Sudheer and Sravani => 7 x5 =35 years and 8x5 = 40 years
After 10 years , their ages will be  = 35+ 10  and 40+10
Ratio of the ages of Sudheer and Sravani after 10 years = 45 : 50  = 9:10

Quantitative Aptitude Questions and  Answers – Problems on Ages
7. The sum of the present ages of a father and his son is 60 years. Six years ago, the father’s age was 5 times the age of the son. What will be the age of son after 7 years?
a)21 years    b)19 years     c)15 years         d)13 years
Answer: A
Explanation:
Let the fathers and sons present age be x and y.
Given sum of the ages of father and son is 60 years =x+y=60
Six years ago, fathers age was 5 times the age of the son => F =5 x S
Ratio of their ages was = 5:1
Six years ago. Sum of the their ages = 60 – (2 x6) =48
Age of the son , 6 years ago = 48 x
1 / 6
= 8 years
Present age of son = 8 years + 6 = 14 years
Age of the son after 7 years = 14 +7 = 21 years

Aptitude Problems on Ages – GMAT Word Problems
8. The age of Sharma and Tripathi differ by 18 years. 6 years ago, Sharma was 3 times as old as Tripathi. What is the present age of Sharma?
a)28 years    b)30 years      c)32 years         d)33 years
Answer :A
Explanation : The difference between the ages of Sharma and Tripathi is 18 years.
The age difference is always same.
6 years ago, ratio of the ages of Sharma and Tripathi => Sharma= 3 Tripathi => 3:1
 Their age difference is 3x-x = 2x = 18 years =>x = 9 years
6 years ago ,  age of Sharma = 3x = 3 x 9 =  27 years.
  Present age of Sharma=  27+ 6 = 33 years.

Aptitude Questions with Explanations : GRE Word Problems
9. One year ago, the ratio of ages of A and B was 6:7. After 4 years, their ratio of the ages will be 7:8. What is present age of B ?
a)30 years         b)36 years    c)40 years         d)42 years
Answer :B
Explanation: One year ago, their ages were be 6x and 7x.
Present ages of A and B are 6x+1 and 7x+1
 After 4 years, age of A will be 6x+1+4  and age of B will be 7x+1+4 =>6x+5 and 7x+5.
After 4 years, their ages will be in the ratio 7:8.
A age after 4 years/B’s age after 4 years =
7 / 8
=>
6x+5 / 7x+5
=
7 / 8
 
=>48x+ 40=49x+35  =>x=5
Present age of B = 7x+1 = 7x5+1 =36.

Aptitude Questions with Solutions : Problems on Ages 10
10. Present ages of A and B are in the ratio 6:7 respectively. 8 years hence, the ratio of the ages will be 8:9 respectively. What is the present age of A ?
a)24 years     b)28 years     c)36 years          d)40 years
Answer : A
Explanation:  Let the present ages of A and B be 6x and 7x years.
After 8 years, their ages will be 6x+8 and 7x+8.
After 8 years, their ages will be in the ratio 8:9.
A ‘s age after 8 years/B’s age after 8 years =8/9
=>
6x+8 / 7x+8
=
8 / 9
 
=>54x+ 72=56x+64  =>2x=8=>x=4
Present age of A = 6x= 6 x 4 =24 years.