Question : A certain sum was to be divided between A and B in the ratio 8 : 5. However, by mistake, it was divided in the ratio 5 : 8. Thus, A gets INR 300 less than his original share. Find the sum.
Option 1: INR 2,600
Option 2: INR 1,500
Option 3: INR 1,300
Option 4: INR 600
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Correct Answer: INR 1,300
Solution :
Let $x$ be the original amount.
A gets $8x$ and B gets $5x$.
By mistake A gets $5x$ and B gets $8x$.
Now A gets Rs. 300 less than the original.
According to the question,
$8x-5x=300$
$⇒3x=300$
$⇒x = 100$
Total sum = $8x+5x$ = $13x$ = Rs. 1300
Hence, the correct answer is INR 1,300.
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