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Mathematics

There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the collection is ₹8.50, how many of each are there?

Linear Equations

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Answer

Let x be the no. of 20 paise coins and y be the no. of 25 paise coins.

x + y = 38 …….(i)

Total value of coins = 0.2x + 0.25y.

Given, total value = ₹8.50

⇒ 0.2x + 0.25y = 8.50 …….(ii)

Multiplying (ii) by 4 we get,

⇒ 0.8x + y = 34 …….(iii)

Subtracting (iii) from (i) we get,

⇒ x + y - (0.8x + y) = 38 - 34

⇒ 0.2x = 4

⇒ x = 40.2\dfrac{4}{0.2}

⇒ x = 402\dfrac{40}{2}

⇒ x = 20.

Substituting value of x in (i) we get,

⇒ 20 + y = 38

⇒ y = 38 - 20

⇒ y = 18.

Hence, no. of 25 paise coins = 18 and no. of 20 paise coins = 20.

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