# There are total 36 coins with raj. Out of them there are 25 paise coin, 10 paise coin and 5paise coins.total money with raj is rs 3. Find the no. Of coins. by ratio method

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by hemi

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by hemi

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Let there be m of 25p coins, and p number of 5paise.

Then there are n = 36 - m - p number of 10p coins.

Assume that there is at least 1 of each type of coin.

Their total value in paise is :

25 m + 10 n + 5 p = 300 paise

25 m + 10 (36 - m - p) + 5 p = 300

5 p = 15 m + 60

p = 3 m + 12

As m >= 1, p >= 15 and p is a multiple of 3. m , n , p are all integers.

m = 1 p = 15 n = 36 - 15 - 1 = 20

m = 2 p = 18 n = 16

m = 3 p = 21 n = 12

m = 4 p = 24 n = 8

m = 5 p = 27 n = 4

So there are five combinations of coins possible.

Then there are n = 36 - m - p number of 10p coins.

Assume that there is at least 1 of each type of coin.

Their total value in paise is :

25 m + 10 n + 5 p = 300 paise

25 m + 10 (36 - m - p) + 5 p = 300

5 p = 15 m + 60

p = 3 m + 12

As m >= 1, p >= 15 and p is a multiple of 3. m , n , p are all integers.

m = 1 p = 15 n = 36 - 15 - 1 = 20

m = 2 p = 18 n = 16

m = 3 p = 21 n = 12

m = 4 p = 24 n = 8

m = 5 p = 27 n = 4

So there are five combinations of coins possible.