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.
Advertisements
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.
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.
An employer finds that if he increases the weekly wages of each worker by Rs. 5 and employs five workers less, he increases his weekly wage bill from Rs. 3,150 to Rs. 3,250. Taking the original weekly wage of each worker as Rs. x; obtain an equation in x and then solve it to find the weekly wages of each worker.
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.
A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
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.
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
