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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