There are some 25 paise coins and some 50 pai | vedclass

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Question

(A) Let the number of $25$ paise coins be $x$ and the number of $50$ paise coins be $y$.According to the problem,the total number of coins is $100$,so

Vedclass · Accepted Answer

$25$ paise: $30$,$50$ paise: $70$

Vedclass · Answer

(A) Let the number of $25$ paise coins be $x$ and the number of $50$ paise coins be $y$.According to the problem,the total number of coins is $100$,so $x + y = 100$ (Equation $1$).The value of $x$ coins of $25$ paise is $0.25x$ rupees,and the value of $y$ coins of $50$ paise is $0.50y$ rupees.The total amount is Rs. $42.50$,so $0.25x + 0.50y = 42.50$ (Equation $2$).Multiply Equation $1$ by $0.25$: $0.25x + 0.25y = 25$ (Equation $3$).Subtract Equation $3$ from Equation $2$: $(0.25x + 0.50y) - (0.25x + 0.25y) = 42.50 - 25$.This simplifies to $0.25y = 17.50$,so $y = 17.50 / 0.25 = 70$.Substitute $y = 70$ into Equation $1$: $x + 70 = 100$,so $x = 30$.Therefore,there are $30$ coins of $25$ paise and $70$ coins of $50$ paise.

There are some $25$ paise coins and some $50$ paise coins in a bag. The total number of coins is $100$ and the total amount in the bag is Rs. $42.50$. Find the number of coins of each value in the bag.

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