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Mathematics

A lady has 25-P and 50-P coins in her purse. If in all she has 80 coins totalling ₹ 25, how many coins of each kind does she have ?

Linear Equations

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Answer

Let Number of 25-P coins be x and number of 50-P coins be y.

Given,

Total number of coins = 80,

⇒ x + y = 80

⇒ x = 80 - y     ………(1)

Given,

Total value = ₹ 25 = 2500 paise,

⇒ 25x + 50y = 2500     …….(2)

Substituting value of x from equation (1) in 25x + 50y = 2500, we get :

⇒ 25x + 50y = 2500

⇒ 25(80 - y) + 50y = 2500

⇒ 2000 - 25y + 50y = 2500

⇒ -25y + 50y = 2500 - 2000

⇒ 25y = 500

⇒ y = 50025\dfrac{500}{25}

⇒ y = 20.

Substituting value of y in equation (1), we get :

⇒ x = 80 - y

⇒ x = 80 - 20

⇒ x = 60.

Hence, number of 25-P coins = 60 and number of 50-P coins = 20.

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