Advertisements
Advertisements
Question
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.
Solution
Original weekly wage of each worker = Rs. x
Original weekly wage bill of employer = Rs. 3150
Number of workers = `3150/x`
New weekly wages of each worker = Rs. (x + 5)
New weekly wage bill of employer = Rs. 3250
Number of workers = `3250/(x + 5)`
From the given condition,
`3150/x - 5 = 3250/(x + 5)`
`(3150 - 5x)/x = 3250/(x + 5)`
3150x – 5x2 + 15750 – 25x = 3250x
–5x2 + 15750 – 125x = 0
x2 + 25x – 3150 = 0
x2 + 70x – 45x – 3150 = 0
x(x + 70) – 45(x + 70) = 0
(x + 70)(x – 45) = 0
x = –70, 45
Since, wage cannot be negative, x = 45.
Thus, the original weekly wage of each worker is Rs. 45
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?
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.
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.
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?
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.
Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'.
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
