Question

A number 30000 is increased successively by 10%, 20% and 30%. Find the overall increase in percentage.

• A. 65.6%
• B. 71.6%
• C. 61.6%
• D. 75.6%

Answer 1

Answer:

B. 71.6%

The overall increase is 71.6%.

Note that the initial number (30,000) does not change the percentage result, as successive percentage increases compound regardless of the starting value.

1. Calculate the compounding multipliers:

   • A 10% increase means multiplying by $1 + 0.10 = \mathbf{1.10}$

   • A 20% increase means multiplying by $1 + 0.20 = \mathbf{1.20}$

   • A 30% increase means multiplying by $1 + 0.30 = \mathbf{1.30}$

2. Find the effective overall multiplier:
   $\text{Overall Multiplier} = 1.10 \times 1.20 \times 1.30$

   • First two increases: $1.10 \times 1.20 = 1.32$

   • Final increase: $1.32 \times 1.30 = \mathbf{1.716}$

3. Convert the multiplier back to a percentage increase:
   $\text{Overall Increase} = (1.716 - 1) \times 100 = \mathbf{71.6\%}$