a man bought a number of bicycles for rs 10000. he kept one for his own use and then sold the rest at a price of rs 50 more than the cost price. besides getting his own bicycle for nothing he made a profit of rs 450. how many bicycles did he buy?
Answers
Answer:
20
Step-by-step explanation:
Let the number of bicycles he bought for 10000 be x.
∴ Cost price of each bicycle = (10000/x)
Given that the man kept one for his own use.
∴ Number of bicycles sold = x - 1.
Selling price of each bicycle = (10000/x + 50)
According to the given condition,
⇒ (x - 1) + (10000/x + 50) - 10000 = 450
⇒ (x - 1) + (10000 + 50x/x) = 450 + 10000
⇒ 10000x + 50x² - 10000 - 50x = 10450x
⇒ 50x² - 500x - 10000 = 0
⇒ x² - 10x - 200 = 0
⇒ x² - 20x + 10x - 200 = 0
⇒ x(x - 20) + 10(x - 20) = 0
⇒ (x - 20)(x + 10) = 0
⇒ x = 20,-10{∴ number of bicycles cannot be negative}
⇒ x = 20.
Therefore, the number of bicycles he bought = 20.
Hope it helps!
Answer:
Number of cycles is 20.
Step-by-step explanation:
Let number of bicycles bought be x .
So here C.P of x cycles = 10,000 .
∴ C.P of 1 cycle = 10,000 / x
One vehicle is not sold and rest are sold.
So x - 1 cycles are sold .
Now S.P of 1 cycles = 50 more than 10,000 / x
= > 50 + 10,000 / x
S.P = C.P + Profit .
So , S.P = 10,000 + 450
= > S.P = 10,450
So : S.P of x - 1 cycles = 10,450
( x - 1 )( 50 + 10,000/x ) = 10450
= > 50 x + 10,000 - 50 - 10,000 / x = 10450
= > 50 x² + 10,000 x - 10,000 = 10500 x
= > 50 x² - 500 x - 10,000 = 0
= > x² - 10 x - 200 = 0
= > x² - 20 x + 10 x - 200 = 0
= > x ( x - 20 ) + 10 ( x - 20 ) = 0
= > ( x + 10 )( x - 20 ) = 0
x = 20
x = - 10
But no of cycle can't be -ve.