Question

The ratio of the incomes of A and B in 2019 was 5 : 4. The ratio of their individual incomes in 2019 and 2020 were 4 : 5 and 2 : 3, respectively. If the total income of A and B in 2020 was ₹7,05,600, then what was the income (in ₹) of B in 2020?

• A. 3,56,000
• B. 3,60,000
• C. 3,46,500
• D. 3,45,600

Hint:

In such ratio problems, use algebra to relate the incomes and solve for the unknown values.

Answer 1

The Correct Option is D

Let the income of A and B in 2019 be \( 5x \) and \( 4x \), respectively.
For 2020, the income of A and B will be \( \frac{5}{4} \times 5x = \frac{25x}{4} \) and \( \frac{3}{4} \times 4x = 3x \), respectively.
The total income in 2020 is ₹7,05,600, so: \[ \frac{25x}{4} + 3x = 7,05,600 \] Simplifying this equation: \[ \frac{25x + 12x}{4} = 7,05,600 \] \[ \frac{37x}{4} = 7,05,600 \] \[ x = 7,05,600 \times \frac{4}{37} = 76,800 \] Thus, the income of B in 2020 is: \[ 3x = 3 \times 76,800 = 3,45,600 \] Thus, the correct answer is 3,45,600.