# Problems on Ages Quiz Set 008

### Question 1

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.

### Question 2

The ratio of ages of P and Q today is \${29/40}\$. After 6 years, their ages will be in the ratio \${151/206}\$. What is the age of P today?

A

145 years.

B

146 years.

C

144 years.

D

147 years.

Soln.
Ans: a

Let the ages of P and Q be 29x and 40x. After 6 years the ratio would be \${29x + 6}/{40x + 6}\$ = \${151/206}\$. Solving, we get x = 5. So age of P = 29 × 5 = 145.

### Question 3

The ratio of ages of P and Q today is \${14/47}\$. After 6 years, their ages will be in the ratio \${5/16}\$. What is the age of P today?

A

84 years.

B

85 years.

C

83 years.

D

86 years.

Soln.
Ans: a

Let the ages of P and Q be 14x and 47x. After 6 years the ratio would be \${14x + 6}/{47x + 6}\$ = \${5/16}\$. Solving, we get x = 6. So age of P = 14 × 6 = 84.

### Question 4

P is 11 years older than Q, and Q's age is 3 times the age of R. If the sum of their ages today is 53, then what is the age of Q?

A

18 years.

B

19 years.

C

17 years.

D

20 years.

Soln.
Ans: a

Let the age of R be x. Then the age of Q is 3x, and that of P is 3x + 11. Adding the three ages, (3x + 11) + 3x + x = 53. Solving, we get x = 6. So the age of Q is 3x = 18 years.

### Question 5

The square root of twice my present age is equal to the sum of the square roots of my ages 10 years back and 10 years hence. What is my present age?

A

10 years.

B

11 years.

C

9 years.

D

20 years.

Soln.
Ans: a

Let the present age be x. Then \$√(x - 10) + √(x + 10)\$ = \$√{2x}\$. Squaring both sides, \$(√(x - 10))^2 + (√(x + 10))^2 + 2√{x^2 - 10^2}\$ = \$2x\$ which gives \$x - 10 + x + 10 + 2√{x^2 - 10^2}\$ = \$2x\$. Cancelling, and simplifying, \$2√(x^2 - 100) = 0\$, which leads to x = 10 years. 