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 following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Solve the equation `3/(x+1)-1/2=2/(3x-1);xne-1,xne1/3,`
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
Two numbers differ by 3 and their product is 504. Find the number
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
Solve the following equation: 3x2 + 25 x + 42 = 0
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
