A cash box holds ₹10, ₹20 and ₹50 notes worth ₹500 in all. There are 3 more ₹20 notes than ₹10 notes, and the number of ₹50 notes is half the number of ₹10 notes. How many notes are in the box?

Explanation

1. 01

   Let there be $t$ notes of ₹10. Then there are $t + 3$ of ₹20 and $\frac{t}{2}$ of ₹50.

2. 02

   Value: $10t + 20(t + 3) + 50 \times \frac{t}{2} = 500$, i.e. $55t + 60 = 500$.

3. 03

   $55t = 440$, so $t = 8$: 8 notes of ₹10, 11 of ₹20 and 4 of ₹50.

4. 04

   Total $= 8 + 11 + 4 = 23$ notes. (Check: $80 + 220 + 200 = 500$.)