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P bought a flat and sold it to Q earning a profit of 15%. Q also sold it to R, thereby earning a profit of 20%. In order to earn a profit of 25%, R had to sell the flat for Rs. 16.56 lakhs. At what price did P bought the flat?

P bought a flat and sold it to Q earning a profit of 15%. Q also sold it to R, thereby earning a profit of 20%. In order to earn a profit of 25%, R had to sell the flat for Rs. 16.56 lakhs. At what price did P bought the flat? Correct Answer Rs. 9.6 lakhs

Shortcut TrickLet the cost price of the flat for P be P.

P × (100 + 15)/100 × (100 + 20)/100 × (100 + 25)/100 = 16.56

⇒ P × 115/100 × 120/100 × 125/100 = 16.56

⇒ P = (16.56 × 20 × 5 × 4)/(23 × 6 × 5)

⇒ 9.6 Lakhs.

∴ The cost price for P is 9.6 Lakhs.

Traditional method:

Let P bought the flat of Rs. ‘x’ lakhs

∵ P earned a profit of 15%,

⇒ Q bought the flat for = x + 15% of x = Rs. 1.15x lakhs

∵ Q earned a profit of 20%,

⇒ R bought the flat for = 1.15x + 20% of 1.15x = 1.15x + 0.23x = Rs. 1.38x lakhs

Now, in order to earn a profit of 25%, R had to sell the flat for Rs. 16.56 lakhs,

⇒ 1.38x + 25% of 1.38x = 16.56

⇒ 1.38x + 0.345x = 16.56

⇒ 1.725x = 16.56

⇒ x = 16.56/1.725 = 9.6 lakhs

∴ P bought the flat for Rs. 9.6 lakhs

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