Question

A lady has 25p and 50p coin in her purse. If in all she has 40 coins totaling Rs.12.50, find the number of coins of each type she has.
A. x = 40(25p coins) and y = 15(50p coins)
B. x = 15(25p coins) and y = 20(50p coins)
C. x = 30(25p coins) and y = 10(50p coins)
D. x = 10(25p coins) and y = 30(50p coins)

Answer 1

Hint: Before solving the question, we try to understand the number of coins in Re.1.
According to the question it discusses two types of coin 25p and 50p. For the 25p this is the fourth part of Re.1. So, the number of coins of 25p in Re.1 will be 4. Same for the 50p this is the second part or half part of Re.1. So, the number of coins of 50p in Re.1 will be 2.
We will make the equation for 25p and 50p in terms of x and y by help the condition from the question there will be two equations after making this solve those equations by the linear method and find the value of x and y, and get the total number of coins individually.

Complete step by step solution:
Let the number of coins of 25p = x
And the number of coins of 50p = y
Total rupees she has Rs.$12.50 = 12.50 \times 100$
$ = 1250\,paise$
According to the question,
$x + y = 40$ ………….. eq. (i)
And
$25x + 50y = 1250$ ……………. eq. (ii)
Solving by elimination method
$\therefore (eq.(i) \times 25) = eq.(ii)$
\[\begin{gathered}
  \,\,\,25x + 25y = 1000 \\
  \,\,\,25x + 50y = 1250 \\
   - \,\,\,\,\,\,\,\,\, - \,\,\,\,\,\,\,\,\,\,\,\,\,\, - \\
=> \,\,\,\,\,\,\,\,\,\,\, - 25y = - 250 \\
\end{gathered} \]
                                     y = 10
On putting the value of y in equation (i)
$\begin{gathered}
  x + y = 40 \\
  x + 10 = 40 \\
  x = 30 \\
\end{gathered} $
i.e. No. of 25 paise coins are 30.
      No. of 50 paise coins are 10.

∴ Option (C) is correct

Note: Another way to solve the above question
Let number of coins of 25 paise = x
Then number of coins of 50 paise = 40-x
$\because $ Total number of coins = 40.
Now, according to the question
$\begin{gathered}
  0.25x + 0.50(40 - x) = 12.50 \\
  0.25x + 20 - 0.50x = 12.50 \\
   - .25x = 12.50 - 20 \\
   - 0.25x = - 7.50 \\
  x = 30 \\
  \therefore y = 40 - x \\
  y = 10 \\
\end{gathered} $