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
B
789
C
978
D
987

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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