# Problems on Ages Quiz Set 001

### Question 1

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.

### Question 2

Mr. X became a voter at the age of 18. He got married at the age of 20. What was his average age during these two points of his life?

A

19 years.

B

20 years.

C

18 years.

D

2 years.

Soln.
Ans: a

The average is simply \${18 + 20}/2\$ = 19 years.

### Question 3

The sum of ages of two friends is 23, whereas the product of their ages is 126. What is the sum of squares of their ages?

A

277 years.

B

278 years.

C

276 years.

D

279 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 23, and xy = 126. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 23^2 - 2 × 126\$ = 277.

### Question 4

My present age is 1287 times the reciprocal of my age 6 years back. What is my present age?

A

39 years.

B

40 years.

C

38 years.

D

41 years.

Soln.
Ans: a

Let the present age be x. Then \$x = 1287/{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)\$ = 1287. This can now be solved to give x = 39 years.

### Question 5

After 5 years from today the ages of three friends will be in an AP(arithmetic progression), and their sum would be 72. What is the age of the middle friend today?

A

19 years.

B

20 years.

C

18 years.

D

21 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 = 72. We get a = 72/3 = 24. So, the age of the middle friend today is a - 5 = 19 years.