A building construction work can be completed | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the time taken by mason $A$ alone to complete the work be $x$ days. Then,mason $B$ alone takes $x+24$ days.Work done by $A$ in $1$ day $= \fra

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) Let the time taken by mason $A$ alone to complete the work be $x$ days. Then,mason $B$ alone takes $x+24$ days.Work done by $A$ in $1$ day $= \frac{1}{x}$.Work done by $B$ in $1$ day $= \frac{1}{x+24}$.Work done by $A+B$ in $1$ day $= \frac{1}{22.5} = \frac{1}{45/2} = \frac{2}{45}$.So,$\frac{1}{x} + \frac{1}{x+24} = \frac{2}{45}$.$\frac{x+24+x}{x(x+24)} = \frac{2}{45} \implies \frac{2x+24}{x^2+24x} = \frac{2}{45}$.$45(x+12) = x^2+24x \implies 45x + 540 = x^2 + 24x$.$x^2 - 21x - 540 = 0$.$(x-36)(x+15) = 0$.Since time cannot be negative,$x = 36$ days.

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

Similar Questions

The number of real roots of the equation $\frac{P^2}{x} + \frac{Q^2}{x - 1} = 1$,where $P$ and $Q$ are non-zero real numbers,is

The value of $4+\frac{1}{5+\frac{1}{4+\frac{1}{5+\frac{1}{4+\ldots \ldots \infty}}}}$ is

Let $\alpha, \alpha^2$ be the roots of $x^2 + x + 1 = 0$. Then the equation whose roots are $\alpha^{31}, \alpha^{62}$ is:

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module