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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 $(A).$

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 $(A).$