# Problems on Ages Quiz Set 011

### Question 1

My present age is 1330 times the reciprocal of my age 3 years back. What is my present age?

A

38 years.

B

39 years.

C

37 years.

D

40 years.

Soln.
Ans: a

Let the present age be x. Then \$x = 1330/{x - 3}\$. 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 - 3)\$ = 1330. This can now be solved to give x = 38 years.

### Question 2

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 14 years back, if the age of the mother today is 50 years?

A

11 years.

B

12 years.

C

10 years.

D

13 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 50/2 = 25 years. And, 14 years back the age of the daughter was 25 - 14 = 11 years.

### Question 3

The sum of reciprocals of my ages 2 years back and 2 years later is \${74/1365}\$. What is my present age?

A

37 years.

B

38 years.

C

36 years.

D

39 years.

Soln.
Ans: a

Let the present age be x. Then \$1/{x + 2} + 1/{x - 2}\$ = \${74/1365}\$. 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 \${2x}/{x^2 - 4}\$ = \${74/1365}\$. This can now be solved to give x = 37 years.

### Question 4

After 5 years from today the ages of three friends will be in an AP(arithmetic progression), and their sum would be 114. What is the age of the middle friend today?

A

33 years.

B

34 years.

C

32 years.

D

35 years.

Soln.
Ans: a

Let the ages after 5 years be a - d, a and a + d. The sum is given to us. So (a - d) + a + (a + d) = 3a = 114. We get a = 114/3 = 38. So, the age of the middle friend today is a - 5 = 33 years.

### Question 5

The ratio of present ages of two monuments A and B is \$2{2/9}\$. After 8 years later the age of A will be 188 years. What is the present age of B?

A

81 years.

B

72 years.

C

63 years.

D

90 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${20/9}\$, which is same as: \$2{2/9}\$. So we can write the present ages of A and B, respectively, as 20r and 9r years. 8 years later the age of A is \$20r + 8 = 188\$ which gives r = 9. The age of B, therefore, is 9r = 9 × 9 = 81 years.