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Question

A bag contains one rupee $$50$$ paise and $$25$$ paise coins in the ratio $$5  : 6  : 8$$. If the total amount is Rs.$$420$$, find the total number of coins.


A
798
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B
789
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C
978
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D
987
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Solution

The correct option is A $$798$$
$$\Rightarrow$$  The ratio of $$Rs.1$$, $$50$$ paise and $$25$$ paise coins is $$5:6:8$$
$$\therefore$$   Number of $$Rs.1$$ coins = $$5x$$.
$$\Rightarrow$$  Number of $$50\,paise$$ coins = $$6x$$
$$\Rightarrow$$  Number of $$25\,paise$$ coins = $$8x$$.
$$\therefore$$  Value of $$5x$$ $$Rs.1$$ coins = $$Rs.1\times 5x=Rs.5x$$.
$$\Rightarrow$$  Value of $$6x$$ $$50\,paise$$ coins = $$6x\times 50\,paise=Rs.\dfrac{6x\times 50}{100}=Rs.3x$$
$$\Rightarrow$$  Value of $$8x$$  $$25\,paise$$ coins = $$8x\times 25\,paise=Rs.\dfrac{8\times 25}{100}=Rs.2x$$
$$\Rightarrow$$  Total amount = $$Rs.420$$
$$\therefore$$  $$5x+3x+2x=420$$
$$\therefore$$  $$10x=420$$
$$\therefore$$  $$x=\dfrac{420}{10}=42$$
$$\therefore$$  Number of $$Rs.1$$ coins = $$5\times 42=210$$
$$\therefore$$  Number of $$50\,paise$$ coins = $$6\times 42=252$$
$$\therefore$$  Number of $$25\,paise$$ coins = $$8\times 42=336$$
$$\Rightarrow$$  Total number of coins = $$210+252+336=798$$

Mathematics

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