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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 cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then find the value of x. Quantity 2: By selling a basket for 19.50, a shopkeeper gains 30%. For how much should he sell it to gain 40%? Quantity 3: An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 25/2% on it. Find the cost price of the article.

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 cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then find the value of x. Quantity 2: By selling a basket for 19.50, a shopkeeper gains 30%. For how much should he sell it to gain 40%? Quantity 3: An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 25/2% on it. Find the cost price of the article. Correct Answer If Quantity 3 is maximum

Quantity 1:

Let C.P. of each article be Rs. 1

⇒ C.P. of x articles = Rs. x

S.P. of x articles = Rs. 20

Profit = Rs. (20 – x)

∴ (20 – x)/x × 100 = 25           

⇒ 2000 – 100x = 25x

⇒ 125x = 2000

 x = 16

Short trick

S.P = 20

C.P = x

Profit % = 25

⇒ x × 125 /100 = 20

x = 2000/125 = 16

Quantity 2:

CP = {100/(100 + P)} x SP

CP = {(19.50 × 100)/130} = Rs. 15

To gain 40% profit

∴ SP = {CP × (100 + profit)/100}

SP = (140 × 15)/100 = Rs. 21

Quantity 3:

Let the cost price of the article = Rs. x

S.P. at 10% loss = 0.9x

According to question if it is sold by 9 more there will be gain of 25/2 %

⇒ 0.9 x + 9 = x × (100 + 25/2)/100

⇒ 0.9 x + 9 = 225x/200

⇒ 180 x + 1800 = 225x

⇒ 45x = 1800

x = 40

Short trick

Let CP = 100

SP = 90, is being sold at 10% loss

New selling price is being sold at 25/2% gain then when SP is 9 more

⇒ Rs. 9 covered 10% loss and 25/2 % profit of the article

⇒ 10% + 12.5 % = 9

⇒ 22.5% ≡ 9

⇒ 100% = 40

Comparing all three quantities we, get quantity 3 > quantity 2 > quantity 1

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