Solving for ₹2 and ₹5 Coins

Let the number of ₹2 coins be '$x$' and the number of ₹5 coins be '$y$'.

Formulating Equations

We are given two conditions:

• Total number of coins: $x + y = 60$
• Total amount of money: $2x + 5y = 240$

Calculating Coin Counts

We can solve this system of linear equations. From the first equation, express '$x$' in terms of '$y$':

$x = 60 - y$

Substitute this expression for '$x$' into the second equation:

$2(60 - y) + 5y = 240$

Simplify and solve for '$y$':

$120 - 2y + 5y = 240$

$120 + 3y = 240$

$3y = 240 - 120$

$3y = 120$

$y = \frac{120}{3}$

$y = 40$

Now substitute the value of '$y$' back into the equation for '$x$':

$x = 60 - 40$

$x = 20$

Verifying the Solution

Check if the calculated values satisfy the original conditions:

• Total coins: $20 + 40 = 60$ (Matches)
• Total amount: $(2 \times 20) + (5 \times 40) = 40 + 200 = 240$ (Matches)

Thus, Rakesh has 20 coins of ₹2 and 40 coins of ₹5.