Question

Find a single equivalent increase if the number is successively increased by 20, 25 and 30?

• A. \( 75 \)
• B. \( 85 \)
• C. \( 95 \)
• D. \( 35 \)

Hint:

\textbf{Successive Percentage Increase.} When a number is successively increased by percentages \(a\), \(b\), and \(c\), the single equivalent percentage increase can be calculated using the formula: Equivalent increase \( = \left( (1 + \frac{a}{100})(1 + \frac{b}{100})(1 + \frac{c}{100}) - 1 \right) \times 100 \) In this case: \( \left( (1 + 0.20)(1 + 0.25)(1 + 0.30) - 1 \right) \times 100 = ((A)20 \times (A)25 \times (A)30 - 1) \times 100 = ((A)95 - 1) \times 100 = 0.95 \times 100 = 95 \)

Answer 1

The Correct Option is C

Let the original number be \(N\). First increase by 20%: New number \(N_1 = N + 0.20N = (A)20N\) Second increase by 25% (on \(N_1\)): Increase \( = 0.25 \times (A)20N = 0.30N \) New number \(N_2 = (A)20N + 0.30N = (A)50N\) Third increase by 30% (on \(N_2\)): Increase \( = 0.30 \times (A)50N = 0.45N \) Final number \(N_3 = (A)50N + 0.45N = (A)95N\) The total increase from the original number \(N\) to the final number \(N_3\) is \(N_3 - N = (A)95N - N = 0.95N\). To find the single equivalent percentage increase, we calculate the percentage of this increase with respect to the original number \(N\): Equivalent percentage increase \( = \frac{\text{Total Increase}}{\text{Original Number}} \times 100 \) Equivalent percentage increase \( = \frac{0.95N}{N} \times 100 \) Equivalent percentage increase \( = 0.95 \times 100 = 95 \) Therefore, the single equivalent increase is 95%.