Question

A number 24000 is increased successively by 15% , 25 % and 20%. Find the overall increase in percentage.

• A. 75%
• B. 80%
• C. 60%
• D. 72.5%

Answer 1

The correct option is D

72.5%

Given number = 24000

There are 2 ways in which we can solve this problem.

First Method :

Increase by 15% gives : $24000+\frac{15}{100}\times 24000$ = 24000 + 3600 = 27600

Increase by further 25% gives : $27600+\frac{25}{100}\times 27600$ = 27600 + 6900 = 34500

Increase by further 20% gives : $34500+\frac{20}{100}\times 34500$ = 34500 + 6900 = 41400

$\therefore$ overall increase in % = $\frac{41400-24000}{24000}\times 100$

= $\frac{17400}{24000}\times 100$ = 72.5%

Second Method :

Multiplying the Successive increase : Original Number $\times \frac{115}{100}\times \frac{125}{100}\times \frac{120}{100}$

= $24000\times \frac{115}{100}\times \frac{125}{100}\times \frac{120}{100}$

= 41400

$\therefore$ overall increase in % = $\frac{41400-24000}{24000}\times 100$

= $\frac{17400}{24000}\times 100$ = 72.5%