Question : Avi sold a house to Bhargav at a gain of 10% and Bhargav sold it to Chetan at a gain of 20%. If Chetan paid Rs. 2,64,00,000 for it, then at what price must Avi have purchased it?
Option 1: Rs. 2,00,00,000
Option 2: Rs. 2,30,00,000
Option 3: Rs. 2,50,00,000
Option 4: Rs. 1,75,00,000
Correct Answer: Rs. 2,00,00,000
Solution :
Let the price Avi purchased the house for as A.
Avi sold the house to Bhargav at a gain of 10%, so Bhargav bought it for 110% of A which we denote as B.
⇒ B = 1.1A
Bhargav then sold the house to Chetan at a gain of 20%, so Chetan bought it for 120% of 'B', which we denote as C.
⇒ C = 1.2B
We know that Chetan paid Rs. 2,64,00,000 for the house, so C = 2,64,00,000.
Substituting B = 1.1A into the equation C = 1.2B,
⇒ C = 1.2 × 1.1A
⇒ 2,64,00,000 = 1.32A
$\therefore$ A = Rs. 2,00,00,000
Hence, the correct answer is Rs. 2,00,00,000.
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