Advertisements
Advertisements
Question
A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction. Taking the number of articles he bought as x, form an equation in x and solve it.
Solution
Number of articles bought by the trader = x
It is given that the trader bought the articles for Rs. 1200
So, the cost of one article = Rs. `1200/x`
Ten articles were damaged. So, the number of articles left = x – 10
Selling price of each of (x – 10) articles = Rs. `(x - 10) (1200/x + 2)`
Profit = Rs. 60
`∴ (x - 10)(1200/x + 2) - 1200 = 60`
`1200 + 2x - 12000/x - 20 - 1200 = 60`
`2x - 12000/x - 80 = 0`
2x2 – 80x – 12000 = 0
x2 – 40x – 6000 = 0
x2 – 100x + 60x – 6000 = 0
x(x – 100) + 60(x – 100) = 0
(x – 100)(x + 60) = 0
x = 100, – 60
Number of articles cannot be negative.
So, x = 100.
APPEARS IN
RELATED QUESTIONS
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
A stone is thrown vertically downwards and the formula d = 16t2 + 4t gives the distance, d metres, that it falls in t seconds. How long does it take to fall 420 metres?
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Mr. Mehra sends his servant to the market to buy oranges worth Rs. 15. The servant having eaten three oranges on the way, Mr. Mehra pays Rs. 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.
Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.
The total cost price of a certain number of identical articles is Rs. 4800. By selling the articles at Rs. 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
In an auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find:
- the number of rows in the original arrangement.
- the number of seats in the auditorium after re-arrangement.
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by `1/14`. Find the fraction.
Two years ago the ages of Radha and Meena were in the ratio 5 : 2. If the sum of their present ages is 39 years, their ages, 2 years ago, were ______.
