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