Multiple choice

The cost of two books are in the ratio $3\colon 5$. If the cost of each of them increases by $Rs.\,20$, the ratio is altered to $13\colon 21$. What is the initial cost of each of them?

  1. $Rs.\ 240$ and $Rs.\ 400$
  2. $Rs.\ 260$ and $Rs.\ 420$
  3. $Rs.\ 280$ and $Rs.\ 440$
  4. $Rs.\ 200$ and $Rs.\ 360$
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A Correct answer
Explanation

Let costs be 3x and 5x. (3x + 20) / (5x + 20) = 13 / 21. 21(3x + 20) = 13(5x + 20). 63x + 420 = 65x + 260. 2x = 160, x = 80. Costs are 3*80=240 and 5*80=400.

AI explanation

Let the initial costs be 3x and 5x. Adding 20 to each gives the new costs, which are in the ratio 13:21, so (3x + 20) / (5x + 20) = 13/21. Cross-multiplying yields 63x + 420 = 65x + 260, which simplifies to 2x = 160, meaning x = 80. The initial costs are 3 multiplied by 80, which is 240, and 5 multiplied by 80, which is 400.

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