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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. $24, 28, 32$

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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Option A

Let the no of each coins be x

coins : 1x, 0.50x, 0.25x

value : 4 * 1x, 5 * 0.50x, 6 * 0.25x

Total : 4 * 1x + 5 * 0.50x + 6 * 0.25x = 32

4x + 2.5x + 1.5x = 32

8x = 32

x = 4.

value : 4*4, 2.5*4, 1.5*4 => 16,10,6

No. of Coins : 16/1, 10/0.5, 6/0.25 => 16, 20, 24

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