Multiple choice

A lady has a total of Rs. 75 in her purse. The total amount she has is in denominations of 10 paisa, 25 paisa and 50 paisa coins. The ratio of 10 paisa and 25 paisa coins is 5 : 3 and that of 25 paisa and 50 paisa coins is 6 : 5. What is the number of 10 paisa coins?

  1. 90

  2. 120

  3. 150

  4. 210

  5. 300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the ratios 10p:25p = 5:3 and 25p:50p = 6:5, we normalize the ratios to 10p:25p:50p = 10:6:5. Let the number of coins be 10k, 6k, and 5k; the total value is 0.1(10k) + 0.25(6k) + 0.5(5k) = 75, which simplifies to 1k + 1.5k + 2.5k = 75, so 5k = 75 and k = 15. The number of 10 paisa coins is 10 * 15 = 150.

AI explanation

Since the 25 paisa coins are common in both ratios, combine the ratio 5:3 and 6:5 by multiplying the first by 2 to get 10:6. The combined ratio of 10 paisa, 25 paisa and 50 paisa coins is 10:6:5. Let the number of coins be 10x, 6x and 5x, making their total value in rupees 0.10(10x) + 0.25(6x) + 0.50(5x) = 5x. Setting 5x = 75 gives x = 15, so the number of 10 paisa coins is 10x, which is 150.

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