Question

if the price of a bicycle is increased by 9.09% then by 8.33% and then by 7.7% the price became 1274.what is the original price of the bicycle?

Answer 1

If the price of a bicycle is increased by 9.09% then by 8.33% and then by 7.7% the price became 1274.

We have to find the original price of the bicycle.

first we should try to write given percentage in proper format.

9.09 % = 100/11 % ⇒ in fraction, 100/11% = 1/11

8.33 % = 24.99/3 % ≈ 25/3 % ⇒in fraction, 25/3 % = 1/12

7.7 % ≈ 70/9 % ⇒in fraction, 70/9 % = 7/90

take LCM of denominators of all fractions.

i.e., LCM {11, 12, 90} = 1980

so we can assume the original price of the bicycle is 1980x

first (1/11)th part is increased.

so, 1980x + 1/11 × 1980x = 2160x

then, (1/12)th part is increased.

so, 2160x + 1/12 × 2160x = 2340x

then, (7/90)th part is increased.

so, 2340x + (7/90) × 2340x = 2522x

now, 2522x = 1274

⇒x = 1274/2522 = 0.5051 ≈ 0.5

so, the original price = 1980 × 0.5 = 990 Rs.

Therefore the original price of the bicycle is 990 Rs.