Question : The ratio of the incomes of A and B in 2020 was 5 : 4. The ratios of their individual incomes in 2020 and 2021 were 4 : 5 and 2 : 3, respectively. If the total income of A and B in 2021 was INR 7,05,600, then what was the income (in INR) of B in 2021?
Option 1: 3,45,600
Option 2: 2,79,700
Option 3: 3,60,000
Option 4: 4,25,900
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Correct Answer: 3,45,600
Solution : Given: The ratio of income of A and B in 2020 = 5 : 4 The ratio of individual income of A in 2020 and 2021 = 4 : 5 The ratio of individual income of B in 2020 and 2021 = 2 : 3 Now, Let the income of A in 2020 be $5x$. income of B in 2020 = $4x$ According to the question, Let the income of A in 2020 be $4y$. Income of A in 2021 = $5y$ and, Income of B in 2020 = $2z$ Income of B in 2021 = $3z$ Here, $5x=4y⇒y=\frac{5x}{4}$ and $4x=2z⇒z=2x$ Now, income of A in 2021 in terms of $x=5\times \frac{5x}{4} = \frac{25x}{4}$ income of B in 2021 in terms of $x=3\times 2x = 6x$ Now, $A + B = 705600$ $\Rightarrow \frac{25x}{4} + 6x =705600$ $\Rightarrow 49x = 705600\times 4$ $\Rightarrow x=57600$ Income of B in 2021 $=6x = 6\times 57600 = 345600$ Hence, the correct answer is Rs. 3,45,600.
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