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