A number is decreased by 20% to get another number. The number so obtained is increased by 200% to get a third number. The difference of the third number and the original number is what percentage more or less than the difference of second and the third number?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 2)

Answer 1

Given:

A number is decreased by 20% to get another number.

The number so obtained is increased by 200% to get a third number.

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let the first number be Q.

Second number = Q(1 - 20%) = 0.8Q

Third number = 0.8Q(1 + 200%) = 2.4Q

The difference between the third number and the original number = 2.4Q - Q = 1.4Q

The difference between the second and third number = 2.4Q - 0.8Q = 1.6Q

Now, % less = \(\frac {1.6Q - 1.4Q}{1.6Q} \times 100\%\) = 12.5%

∴ The difference between the third number and the original number is 12.5% less than the difference between the second and the third number.