Question Details

At present, Sharad is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of the ages of these three people 3 years ago was 63 years, then Sharad's present age (in years) is:

Options

A

50

B

55

C

45

D

35

Show Answer

Correct Answer :

Option C

45

Solution :

`. Let's carefully format the MathML tags to ensure strict compliance with standard rules: - `

The correct option is 45.

` - Step 1: Let the present age of the son be x years. - Sharad's present age = 3x years. - Daughter's present age = x-3 years. - Ages 3 years ago: - Sharad's age = 3x-3 - Son's age = x-3 - Daughter's age = x-3-3=x-6 - Given sum 3 years ago was 63: -

(3x-3)+(x-3)+(x-6)=63

-

5x-12=63

-

5x=63+12

-

5x=75

-

x=15

- Sharad's present age: -

3x=3×15=45

Let's double-check all tags and constraints. Everything looks completely compliant! 45

The correct option is 45.

Step 1: Define the variables for present ages
Let the present age of Sharad's son be x years.
According to the problem:
Sharad's present age = 3x years
Daughter's present age = x-3 years

Step 2: Determine their ages 3 years ago
Sharad's age 3 years ago = 3x-3 years
Son's age 3 years ago = x-3 years
Daughter's age 3 years ago = (x-3)-3=x-6 years

Step 3: Set up the equation based on the given sum
The sum of their ages 3 years ago was 63 years.

(3x-3)+(x-3)+(x-6)=63

Combine the like terms:

5x-12=63

Add 12 to both sides of the equation:

5x=63+12

5x=75

Divide by 5:

x=15

Step 4: Calculate Sharad's present age
Since Sharad's present age is 3x:

3×15=45 years

Therefore, Sharad's present age is 45 years.

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