Let's solve this step by step:
1. Understanding the relationships:
- A's expenditure is 20% more than B's expenditure.
- B's expenditure is 30% less than C's expenditure.
2. Express B's expenditure in terms of C's expenditure:
- Let \(\( C \)\) be C's expenditure.
- Since B's expenditure is 30% less than C's expenditure, we can write:
\(\[
B = C - 0.30C = 0.70C
\]\)
3. Express A's expenditure in terms of B's expenditure:
- B's expenditure is given as \(\( 0.70C \)\).
- Since A's expenditure is 20% more than B's expenditure, we can write:
\(\[
A = B + 0.20B = 1.20B
\]\)
- Substitute \(\( B \)\) with \(\( 0.70C \)\):
\(\[
A = 1.20 \times 0.70C = 0.84C
\]\)
4. Calculate the percentage by which A's expenditure is less than C's expenditure:
- The difference between C's expenditure and A's expenditure is:
\(\[
C - A = C - 0.84C = 0.16C
\]\)
- To find the percentage by which A's expenditure is less than C's expenditure, we use the formula:
\(\[
\frac{C - A}{C} \times 100\%
\]\)
Substituting \(\( C - A \)\) with \(\( 0.16C \)\) and \(\( C \)\) in the formula:
\(\[
\frac{0.16C}{C} \times 100\% = 0.16 \times 100\% = 16\%
\]\)
So, A's expenditure is 16% less than C's expenditure.
