# Problems on Ages Quiz Set 005

### Question 1

My present age is 315 times the reciprocal of my age 6 years back. What is my present age?

A

21 years.

B

22 years.

C

20 years.

D

23 years.

Soln.
Ans: a

Let the present age be x. Then \$x = 315/{x - 6}\$. At this stage a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation \$x × (x - 6)\$ = 315. This can now be solved to give x = 21 years.

### Question 2

The sum of ages of two friends is 12, whereas the product of their ages is 35. What is the sum of squares of their ages?

A

74 years.

B

75 years.

C

73 years.

D

76 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 12, and xy = 35. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 12^2 - 2 × 35\$ = 74.

### Question 3

The ratio of ages of P and Q today is \${29/59}\$. After 3 years, their ages will be in the ratio \${119/239}\$. What is the age of P today?

A

116 years.

B

117 years.

C

115 years.

D

118 years.

Soln.
Ans: a

Let the ages of P and Q be 29x and 59x. After 3 years the ratio would be \${29x + 3}/{59x + 3}\$ = \${119/239}\$. Solving, we get x = 4. So age of P = 29 × 4 = 116.

### Question 4

When the daughter was born, the age of her mother was same as the daughter's age today. What was the age of the daughter 5 years back, if the age of the mother today is 36 years?

A

13 years.

B

14 years.

C

12 years.

D

15 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 36/2 = 18 years. And, 5 years back the age of the daughter was 18 - 5 = 13 years.

### Question 5

4 years back the ratio of ages of X and Y was \${13/27}\$. The ratio of their ages 3 years from now would be \${10/17}\$. What is the present age of X?

A

17 years.

B

18 years.

C

16 years.

D

19 years.

Soln.
Ans: a

Let their present ages be x and y. Then \${x - 4}/{y - 4} = \$ \${13/27}\$. Similarly, \${x + 3}/{y + 3} = \$ \${10/17}\$. Solving these equations for x and y, we get y = 31, and x = 17 years as the answer. 