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

Answer 1

The Correct Option is B

Step 1: Define the variables 

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

Step 2: Establish the first equation

One year ago, the ratio of their ages was 6:7. Thus, we can write:

\[ \frac{x - 1}{y - 1} = \frac{6}{7} \]

Cross multiplying:

\[ 7(x - 1) = 6(y - 1) \]

Expanding:

\[ 7x - 7 = 6y - 6 \]

Rearranging:

\[ 7x - 6y = 1 \quad \text{(Equation 1)} \]

Step 3: Establish the second equation

Four years hence, the ratio of their ages would be 7:8. Thus, we can write:

\[ \frac{x + 4}{y + 4} = \frac{7}{8} \]

Cross multiplying:

\[ 8(x + 4) = 7(y + 4) \]

Expanding:

\[ 8x + 32 = 7y + 28 \]

Rearranging:

\[ 8x - 7y = -4 \quad \text{(Equation 2)} \]

Step 4: Solve the system of equations

We have the two equations:

• \( 7x - 6y = 1 \) (Equation 1)
• \( 8x - 7y = -4 \) (Equation 2)

Multiply Equation (1) by 8 and Equation (2) by 7:

\[ (8 \times 7x) - (8 \times 6y) = 8 \times 1 \] \[ (7 \times 8x) - (7 \times 7y) = 7 \times (-4) \]

Simplifies to:

\[ 56x - 48y = 8 \quad \text{(Equation 3)} \] \[ 56x - 49y = -28 \quad \text{(Equation 4)} \]

Subtracting Equation (4) from Equation (3):

\[ (56x - 48y) - (56x - 49y) = 8 - (-28) \]

\[ y = 36 \]

Step 5: Conclusion

Thus, Anushka’s present age is 36 years.