A shopkeeper bought 2 chairs in Rs. 900. He sells first chair at \(\frac{5}{4}\) of its cost price and second chair at \(\frac{4}{5}\) of its cost price. If he gains Rs. 90 as a profit then find the cost price of both chairs.

600, 300

1^st chair:

SP =  \(\frac{5}{4}\) × CP

⇒ C.P. : S.P. = 4 : 5

⸫ Profit percent = \(\frac{1}{4}\) × 100 = 25%

II^nd chair:

SP = \(\frac{4}{5}\) × CP

⇒ C.P. : S.P. = 5 : 4

⸫ Loss percent = \(\frac{1}{5}\) × 100 = - 20%

Overall profit = Rs. 90

Overall profit percent = \(\frac{90}{900}\) × 100 = 10% profit

Now, Using allegation method:

Now,

3R = Rs. 900 (given)

1R = 300

Hence,

C.P. of 1st = 2R = 2 × 300 = Rs. 600

C.P. of 2nd = 1R = 1 × 300 = Rs. 300