a man bought a certain number of toys for rs 180.he kept one for own use and sold the rest for one rupee each more than he gave for them.besides getting his own toy for nothing,he made a profit of rs 10.find the number of toys
Answers
let number of toys be x
given that cost price of x toys = Rs 180
So cost price of 1 toy = Rs (180/x)
no of toys he sold = x-1 ( since one he kept for own use)
sales price of 1 toy = cost price of 1 toy + 1
sales price of 1 toy = (180/x) + 1 = (180 +x)/x
sales price of (x-1 ) toy = ( (180 +x)/x) × (x-1)
profit = sales price of (x-1 ) toy - cost price of x toys
10 = ( (180 + x) (x -1 ) /x ) - 180
⇒ 190 = (180x -180 + x² - x)/x
⇒ 190x = 179x -180 + x²
⇒ 0 = 179x -190 x -180 + x²
⇒ x² - 11x - 180 = 0
⇒ x² -20x + 9x - 180 = 0
⇒ x(x- 20) + 9 ( x - 20 ) = 0
⇒ (x + 9 ) ( x - 20 ) = 0
⇒ (x + 9 ) = 0 or ( x - 20 ) = 0
⇒ x = -9 or x = 20
ignoring the negative value
x = 20
number of toys = 20
let number of toys be x
given that cost price of x toys = Rs 180
So cost price of 1 toy = Rs (180/x)
no of toys he sold = x-1 ( since one he kept for own use)
sales price of 1 toy = cost price of 1 toy + 1
sales price of 1 toy = (180/x) + 1 = (180 +x)/x
sales price of (x-1 ) toy = ( (180 +x)/x) × (x-1)
profit = sales price of (x-1 ) toy - cost price of x toys
10 = ( (180 + x) (x -1 ) /x ) - 180
⇒ 190 = (180x -180 + x² - x)/x
⇒ 190x = 179x -180 + x²
⇒ 0 = 179x -190 x -180 + x²
⇒ x² - 11x - 180 = 0
⇒ x² -20x + 9x - 180 = 0
⇒ x(x- 20) + 9 ( x - 20 ) = 0
⇒ (x + 9 ) ( x - 20 ) = 0
⇒ (x + 9 ) = 0 or ( x - 20 ) = 0
⇒ x = -9 or x = 20
ignoring the negative value
x = 20
number of toys = 20