Question

One year ago, the ratio of Siddhi and Anushka’s age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Anushka?

• A. \( 56 \)
• B. \( 36 \)
• C. \( 63 \)
• D. \( 44 \)
• E.

Hint:

For age ratio problems, use the given ratios to form equations and solve the system of equations to find the unknowns.

Answer 1

The Correct Option is B

Step 1: Let the present age of Siddhi be \( x \) years and the present age of Anushka be \( y \) years. 

Step 2: According to the problem, one year ago, the ratio of their ages was 6:7, so we can write the equation: \[ \frac{x - 1}{y - 1} = \frac{6}{7} \] This simplifies to: \[ 7(x - 1) = 6(y - 1) \] \[ 7x - 7 = 6y - 6 \] \[ 7x - 6y = 1 \quad \cdots (1) \] 

Step 3: The second condition given is that four years hence, the ratio of their ages would be 7:8, so: \[ \frac{x + 4}{y + 4} = \frac{7}{8} \] This simplifies to: \[ 8(x + 4) = 7(y + 4) \] \[ 8x + 32 = 7y + 28 \] \[ 8x - 7y = -4 \quad \cdots (2) \] 

Step 4: We now solve the system of linear equations: \[ 7x - 6y = 1 \quad \text{(equation 1)} \] \[ 8x - 7y = -4 \quad \text{(equation 2)} \] Multiply equation (1) by 8 and equation (2) by 7 to eliminate \( y \): \[ 56x - 48y = 8 \quad \text{(equation 3)} \] \[ 56x - 49y = -28 \quad \text{(equation 4)} \] Subtract equation (4) from equation (3): \[ (56x - 48y) - (56x - 49y) = 8 - (-28) \] \[ y = 36 \] 

Step 5: Thus, Anushka's present age is \( y = 36 \). Thus, the correct answer is 36.