1.

Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coinstotalling ? 220, how many coins of each kind does she have.

Answer»

Let the number of 2 rupee coin be x and the number of 5 rupee coin be y.

x + y = 80 . . . . . (1)2x + 5y = 220 . . . . . (2)

(1) × 5

5x + 5y = 400 . . . . . (3)

(3) - (2)

3x = 180=> x = 60

Substituting x in (1),

60 + y = 80=> y = 20

Therefore,

Number of 2 rupee coins = 60Number of 5 rupee coins = 20

Recheck:

20 + 60 = 802(60) + 5(20) = 120 + 100 = 220

Total money= Rs220Total no of coins= 80 x + y = 80 2x + 5y = 220Use diophantine equation x=60 y=202×60=rs1205×20=rs100rs100+rs120=rs22020+60=80coinsAns) Abhraya has 60 2rupee coins and 20 5 rupee coins in her purse.


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