  Question

I have a total of Rs. $$300$$ in coins of denomination Re. $$1$$, Rs. $$2$$ and Rs. $$5$$. The number of Rs. $$2$$ coins is $$3$$ times the number of Rs. $$5$$ coins. The total number of coins is $$160$$. How many coins of each denomination are with me?

A
Number of Re. 1 coins =50; Number of Rs. 2 coins =40; Number of Rs. 5 coins =40  B
Number of Re. 1 coins =70; Number of Rs. 2 coins =70; Number of Rs. 5 coins =19  C
Number of Re. 1 coins =80; Number of Rs. 2 coins =60; Number of Rs. 5 coins =20  D
Number of Re. 1 coins =115; Number of Rs. 2 coins =50; Number of Rs. 5 coins =15  Solution

The correct option is C Number of Re. $$1$$ coins $$= 80$$; Number of Rs. $$2$$ coins $$= 60$$; Number of Rs. $$5$$ coins $$= 20$$Given, Total number of coins $$= 160$$Given that the number of Rs.$$2$$ coins are $$3$$ times the number of Rs. $$5$$ coins.Number of Rs. $$5$$ coins $$= x$$Number of Rs. $$2$$ coins $$= 3x$$Number of Re. $$1$$ coins $$= 160 -(x+3x) = 160 -4x$$Total value of coins $$=$$ Rs. $$300$$So, $$5\times x + 2\times 3x + 1\times (160 -4x) = 300$$$$5x +6x +160 -4x = 300$$$$7x = 140$$$$x = 20$$So, number of Rs. $$5$$ coins $$= 20$$Number of Rs. $$2$$ coins $$= 60$$Number of Re. $$1$$ coins $$=80$$Mathematics

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