Question

A purse contains 25 paise coins and 10 paise coins only. The total amount inside the purse is Rs 8.25 and the number of 25 paise coins is one-third the number of 10 paise coins. Find the total number of coins inside the purse.

Answer 1

Hint: Assume that the number of 25 paise coins is x and the number of 10 paise coins is y. Use the fact that the total amount inside the purse is Rs 8.25 to form an equation in x and y. Use the fact that the number of 25 paise coins is one-third the number of 10 paise coins, to form another equation in x and y. Solve the system of the equations by any of the known methods like elimination method, substitution method etc and hence find the value of x and y. Hence find the total number of the coins in the purse. Verify your answer.

Complete step by step solution:
Let the number of 25 paise coins be x and the number of 10 paise coins be y.
Since the total amount inside the purse is Rs 8.25 = 825 paise, we have
$25x+10y=825$
Dividing both sides of the equation by 5, we get
$5x+2y=165\text{ }\left( i \right)$
Since the number of 25 paise coins is one-third of the number of 10 paise coins, we have
$x=\dfrac{y}{3}$
Multiplying both sides by 3, we get
$y=3x\text{ }\left( ii \right)$
Substituting the value of y from equation (ii), in equation (i), we get
$\begin{align}
  & 5x+2\left( 3x \right)=165 \\
 & \Rightarrow 5x+6x=165 \\
 & \Rightarrow 11x=165 \\
\end{align}$
Dividing both sides by 11, we get
$x=\dfrac{165}{11}=15$
Substituting the value of x in equation (ii), we get
$y=3\left( 15 \right)=45$
Hence the number of 10 paise coins is 45 and the number of 25 paise coins is 15
Hence the total number of coins inside the purse is 45+25 = 70.


Note: Verification:
We can verify the correctness of our solution by checking that the total amount inside the purse adds up to Rs 8.25 and the number of 25 paise coins is one-third the number of 10 paise coins.
We have Total amount inside the purse $=15\times 25+45\times 10=375+450=825\text{ paise}$
Hence the total amount inside the purse is Rs 8.25
Also, we have one-third of number of 10 paise coins $=\dfrac{1}{3}\left( 45 \right)=15$
Hence the number of 25 paise coins is one-third the number of 10 paise coins.
Hence our solution is verified to be correct.