Advertisements
Advertisements
Question
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Advertisements
Solution
Let B alone takes x days to finish the work. Then, B’s one day’s work = 1/x.
Similarly, A alone can finish it in (x - 10) days to finish the work. Then, A’s one day’s work `=1/(x-10)`.
It is given that
A’s one day’s work + B’s one day’s work = (A + B)’s one day’s work
`1/x+1/(x-10)=1/12`
`(x-10+x)/(x(x-10))=1/12`
`(2x-10)/(x^2-10x)=1/12`
x2 - 10x = 12(2x - 10)
x2 - 10x = 24x - 120
x2 - 10x - 24x + 120 = 0
x2 - 34x + 120 = 0
x2 - 30x - 4x + 120 = 0
x(x - 30) - 4(x - 30) = 0
(x - 30)(x - 4) = 0
x - 30 = 0
x = 30
Or
x - 4 = 0
x = 4
But x = 4 is not correct.
therefore, x = 30 is correct
Hence, the time taken by B to finish the work in x = 30 days
APPEARS IN
RELATED QUESTIONS
Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
Find the two consecutive natural numbers whose product is 20.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
`x^2+8x-2=0`
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Solve the following quadratic equation by factorisation.
7m2 = 21m
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Solve equation using factorisation method:
x2 – 10x – 24 = 0
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.
The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.
Solve the following equation by factorisation :
2x2 + ax – a2= 0
The product of two successive integral multiples of 5 is 300. Then the numbers are:
