Question : The ratio of the incomes of A and B in the last year was 4 : 3. The ratios of their individual incomes in the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income in the present year is INR 24.12 lakhs, then the sum of the income (in INR lakhs) of A in the last year and that of B in the present year is:
Option 1: 10.98
Option 2: 20.52
Option 3: 22.17
Option 4: 21.28
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Correct Answer: 20.52
Solution : The ratio of the incomes of A and B last year was 4 : 3. Let the income of A in the last year be $4x$ and B be $3x$. The ratio of income of A from the last year to the present year is 3 : 4. Here, let A's last year's income be $3k$ and present income be $4k$. So, $3k = 4x$ $⇒ k = \frac{4x}{3}$ $\therefore$ Present income $= 4k = 4×\frac{4x}{3}$ The ratio of income of B the last year to the present year is 5 : 6. Here, let B's last year's income be $5z$ and present income be $6z$. So, $5z = 3x$ $⇒ z = \frac{3x}{5}$ $\therefore$ Present income $= 6z = 6×\frac{3x}{5}$ Their total income in the present year is INR 24.12 lakhs. According to the question, $4×\frac{4x}{3}+6×\frac{3x}{5}=24.12$ $⇒\frac{80x+54x}{15}=24.12$ $⇒134x=24.12×15$ $\therefore x=2.7$ lakhs Last year's income of A $=4x=4×2.7=10.8$ lakhs Present year income of B $=6×\frac{3x}{5}=\frac{18×2.7}{5}=9.72$ lakhs Total sum = 10.8 + 9.72 = 20.52 lakhs Hence, the correct answer is 20.52.
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