Question

ANSWER QUESTIONS TO THE FULL
1. After a discount of 12% on the marked price, a shopkeeper still gains 21%. By what per cent is the marked price above cost price.
2. Find a single discount equivalent to two successive discounts of 20% and 10%.
3. Find a single discount equivalent to two successive discounts of 40% and 5%.
4. Find a single discount equivalent to three successive discounts of 20%,5% and 1%.
5. The marked price of a watch is rs 1375. If tax is charged at the rate of 4%, find the total cost of the watch.

Answer 1

Q1. let cp is 100
therefore sp = 121
let mp = x
discount = 12%
sp = 88x/100
now, 88x/100 =121
88x = 12100
x = 12100/88 => x = 137.5
so the mp is 137.5 and cp is 100
the over marked amount is 137.5 - 100 = 37.5
therefore over marked percent = 37.5%
Q2. successive discount = 20% & 10%
let the mark value is 100
therefore sp after discount = (100-20)/100 ×(100-10)/100 × 100. => 8/10 × 9/10 × 100 => 72
the discounted value is 100-72 = 28
so the single equivalent discount is 28/100 × 100 => 28%
Q3. follow the above solution
Q4. let mark value = 100
successive discount = 20, 5 &1
sp after discount = (100-20)/100 × (100-5)/100 × (100-1)/100 ×100 => 80/100 × 95/100 × 99/100 × 100 => 0.8 × 0.95 × 0.99 × 100 => 75.24
therefore discount value is 100-75.24 = 24.76
single discount for these discounts = 24.76/100 × 100 => 24.76%
Q5. mark price = ₹1375
tax = 4%
total cost of watch is ₹1375(104/100) => ₹1375 × 26/25 => ₹55 × 26 =>₹ 1430