Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. Quantity 1: The marked price of a timex sports watch was Rs.720. A man bought the same for Rs. 550.80 after getting two successive discounts, the first being 10%. What was the second discount rate? Quantity 2: The shopkeeper sold his good at half the list price and thus lost 20%. If he had sold on the listed price, find the gain percent. Quantity 3: The timber trader marked his good at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at the discount of 30% on the marked price. Find the total gain.

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. Quantity 1: The marked price of a timex sports watch was Rs.720. A man bought the same for Rs. 550.80 after getting two successive discounts, the first being 10%. What was the second discount rate? Quantity 2: The shopkeeper sold his good at half the list price and thus lost 20%. If he had sold on the listed price, find the gain percent. Quantity 3: The timber trader marked his good at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at the discount of 30% on the marked price. Find the total gain. Correct Answer If Quantity 2 is maximum

Quantity 1:

Let the second discount rate be x%

Then, (100 – x) % of 90% of 720 = 550.80

⇒ (100 – x) / (100) × (90) / (100) × 720 = 550.80

⇒ 100 – x = (55080) / (9 × 72) = 85

⇒ x = 15

Hence the second discount rate is 15%

Short trick

Total discount = 720 – 550.80 = 169.2/720 ×100 = 23.5%

Successive discount formula

Total discount = {(x + y – xy)/100} %

23.5% = (10% + x – 10x/100)

x = 15%

Quantity 2:

let CP of goods = Rs. x

And the list price = Rs. p

And there is 20 % loss, therefore SP = 80% of x = 0.8x

As per the question

0.8 = p/2

⇒ p = Rs. 1.6x

Now, gain percent by selling goods in on listed price = (1.6x – x)/(x) × 100% = 60%

Short trick

Let the List price = 100

SP = 50 ≡ 80% (after 20% loss on CP of 100)

So, 100 ≡ 160

Profit = 60 /100 ×100 = 60 %

Quantity 3:

 Let C.P of whole stock = Rs. 100

Then marked price of whole stock = Rs. 120

⇒ M.P of ½ stock = Rs. 60

⇒ M.P of ¼ stock = Rs. 30

Total S.P = = = Rs. 105

Hence, gain% = (105 – 100) % = 5%

∴ Comparing all three quantities we get Quantity 2 > Quantity 1 > Quantity 3