Question

A number is first decreased by 15% and then increased by 20%. The number so obtained is 78 more than the original number. The original number is :

• A. 3900
• B. 2600
• C. 4500
• D. 5200

Answer 1

Answer:

A. 3900

Let the original number be x.

Decrease by 15%

After 15% decrease:
$x - 0.15x = 0.85x$
Increase by 20%

After 20% increase:
$0.85x + 0.20(0.85x) = 0.85x \times 1.20 = 1.02x$

The final number is 78 more than the original number:
$1.02x = x + 78$

$1.02x - x = 78$
$0.02x = 78$
$x = \frac{78}{0.02} = 3900$

The original number is 3900