Question : The ratio of the incomes of A and B is 3 : 5, whereas the ratio of their expenditures is 4 : 7 respectively. If A and B save INR 16,000 and INR 26,000, respectively, then what is the difference (in INR) between their expenditures?
Option 1: 5400
Option 2: 6800
Option 3: 5000
Option 4: 6000
Correct Answer: 6000
Solution : Let's see the incomes of A and B as I A and I B , and their expenditures as E A and E B . So, A' s saving = I A − E A = 16,000 and B's saving = I B − E B = 26,000 Let the incomes of A and B be 3$k$ and 5$k$ respectively. So, I A = 3$k$ and I B = 5$k$ ⇒ E A = 3$k$ + 16000 and E B = 5$k$ + 26,000 So, according to the question $\frac{3k - 16000}{5k - 26000}= \frac{4}{7}$ ⇒ $21k - 112000 = 20k - 104000$ ⇒ $k= 8000$ So, the incomes of A and B are 24000 and 40000 respectively. E A = 24000 – 16000 = 8,000 E B = 40000 – 26000 = 14,000 $\therefore$ Difference = 14000 – 8000 = 6,000 Hence, the correct answer is 6,000.
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