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How many one rupee coins, $50$ paise coins and $25$ paise coins of which the numbers are proportional to $4, 5$ and $6$ are together worth  ₹$32$?

  1. $16, 20, 24$
  2. $12, 16, 20$
  3. $20, 24, 28$
  4. $24, 28, 32$
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Given that, ratio of  one rupee coins, $50$ paise coins and $25$ paise coins $ = 4:5:6$

Value ratio of 1$00$ paise, $50$ paise and $25$ paise $ = 4 \times 100 : 5 \times 50 : 6 \times 25 = 400:250:150 = 8:5:3$

Now,  ratio of 1$00$ paise, $50$ paise and $25$ paise  $= 8k:5k:3k$

And, $8k+5k+3k =  ₹32$

$\implies 16k = ₹32$

$\implies k = ₹2$

Now, one rupees coins $ = 8k = 16,50$ paise coins $ = 2 \times 5k = 20,$ and $25$ paise coins $ = 4 \times 3k = 24$

So, the correct answer is $(A).$
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