Average problem 3 by Dhaval Furia

Algebra Level 2

Mukesh purchased 10 10 bicycles in 2019 2019 , all at the same price. He sold six of these at a profit of 25 % 25\% and the remaining four at a loss of 25 % 25\% . If he made a total profit of Rs. 2000 2000 , what was his purchase price in Rs of a bicycle?

2000 2000 4000 4000 8000 8000 6000 6000

Dhaval Furia by Dhaval Furia , 26, India

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2 solutions

Let the Cost(CP) of each bicycle be Rs. x. \text{Let the Cost(CP) of each bicycle be Rs. x.}

Six bicycles sold at profit

CP = 6 x =6x

SP = 125 % =125\% of CP

SP = 5 4 × 6 x =\dfrac{5}{4}\times 6x

⟹ \implies SP = 7.5 x =7.5x

Four bicycles sold at loss

CP = 4 x \text{CP}=4x

SP = 75 % of CP \text{SP}=75\% \text{of CP}

SP = 3 4 × 4 x \text{SP}=\dfrac{3}{4}\times 4x

⟹ SP = 3 x \implies \text{SP}=3x

Overall

CP = 10 x \text{CP}=10x

SP = 7.5 x + 3 x = 10.5 x \text{SP}=7.5x+3x=10.5x

⟹ Profit = 10.5 x − 10 x = 0.5 x = Rs. 2000 \implies\text{Profit}=10.5x-10x=0.5x=\text{Rs.} 2000

⟹ x = Rs. 4000 \implies x= \boxed{\text{Rs.}4000}

2 Helpful 1 Interesting 1 Brilliant 0 Confused

Let the purchase price of each bicycle be Rs. a a . Then

6 a ( 1 + 25 100 ) + 4 a ( 1 − 25 100 ) − 10 a 6a(1+\frac{25}{100})+4a(1-\frac{25}{100})-10a

= 2000 ⟹ a = =2000\implies a= Rs. 4000 \boxed {4000} /-

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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