A discount series of 10%, 20% and 40% is equivalent to a single discount of ???

Question

A shopkeeper buys a Printer set listed at Rs.10000 and get 10% and 20% successive discount. He spends 10% of his C.P. on transport. At what price (in rupees) should he sell the Printer set to earn a profit of 10%.

Answer 1

If 2 succesive discounts a% and b%
then net discount = a + b – (ab/100)

If 3 succesive discounts a%, b% and c%
then single discount
= a + b + c – (ab/100 + bc/100 + ca/100 – abc/10000)
In this case,
single discount
= 10 + 20 + 40 – (200/100 + 800/100 + 400/100 – 8000/10000)
= 70 – (14 – 0.8)
= 56.8 %

Answer 2

Say 100 is the price -
1. 1st 10 % discount means the sales price is 90
2. 2nd 20% discount on 90 means sales price is 72 (90-18)
3. 3rd 40% discount on 72 means sales price is 43.2 (72-28.8)

Total discount is 100-43.2 or 56.8%