Question

Avni purchased bicycle after two successive discounts of 10% and 15% respectively. She further sold it to roshni at 20% profit. Roshni sold the same bicycle at 10% loss to harshita. If Roshni purchased the cycle at Rs. 1200 then calculate approximate marked price of cycle before discounts.

1. Rs. 1307
2. Rs. 1460
3. Rs. 1560
4. Rs. 1660
5. Rs. 1760

Answer 1

Correct Answer - Option 1 : Rs. 1307

Given:

C.P. for roshni = Rs. 1200

Successive discounts = 10% and 15%

Profit = 20%

Formula:

Successive discounts: r₁ + r₂ – (r₁r₂/100) = effective r

Profit% = (S.P. – C.P. / C.P.) × 100

S.P. = C.P. (1 + (profit%/ 100))

Calculation:

Avni sold bicycle to roshni at 20% profit

⇒ C.P. of cycle for roshni = Rs 1200

⇒ C.P. of cycle for roshni = S.P. of cycle for avni

⇒Let C.P. of cycle for avni = Rs. X

⇒ S.P. of cycle for avni = X + (20/ 100) X

⇒ S.P. of cycle for avni = 1.20 X

⇒ 1200 = 1.20 X

⇒ X = Rs. 1000

Effective discount = 10 + 15 – (10 × 15/ 100)

⇒ Effective discount = 25 – 1.5

⇒ Effective discount = 23.5%

Let marked price be Rs. Y

⇒ Y – (23.5/ 100) Y = 1000

⇒ Y – 0.235Y = 1000

⇒ 0.765Y = 1000

⇒ Y = 1000/ 0.765

⇒ Y ≈ 1307

∴ Marked price is Rs. 1307