B would have taken 10 , text{hours} more than | vedclass

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

Question

(B) Let the time taken by $A$ to complete the task be $x \, 	ext{hours}$.Then,the time taken by $B$ to complete the task is $(x + 10) \, 	ext{hours}

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) Let the time taken by $A$ to complete the task be $x \, 	ext{hours}$.Then,the time taken by $B$ to complete the task is $(x + 10) \, 	ext{hours}$.Working together,their combined rate of work is $\frac{1}{x} + \frac{1}{x + 10} = \frac{1}{12}$.Solving for $x$: $\frac{x + 10 + x}{x(x + 10)} = \frac{1}{12} \implies 12(2x + 10) = x^2 + 10x$.$24x + 120 = x^2 + 10x \implies x^2 - 14x - 120 = 0$.Factoring the quadratic equation: $(x - 20)(x + 6) = 0$.Since time cannot be negative,$x = 20 \, 	ext{hours}$.Thus,$B$ takes $x + 10 = 30 \, 	ext{hours}$ to complete the whole task.To complete $50 \%$ of the task,$B$ will take $50 \% 	ext{ of } 30 \, 	ext{hours} = 15 \, 	ext{hours}$.

$B$ would have taken $10 \, \text{hours}$ more than what $A$ would have taken to complete a task if each of them worked alone. Working together they can complete the task in $12 \, \text{hours}$. How many $\text{hours}$ would $B$ take to do $50 \%$ of the task?

Similar Questions

$A$ does half as much work as $B$ in $\frac{3}{4}$ of the time. If together they take $18$ days to complete a work,then how much time shall $B$ take to complete it? (in days)

$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?

Amit and Sujit together can complete a data entry assignment in $5$ days. Sujit's speed is $80\%$ of Amit's speed and the total key depressions in the assignment are $5,76,000$. What is Amit's speed in key depressions per hour if they work for $8$ hours a day?

$P$ can do a piece of work in $9$ days. $Q$ is $50\%$ more efficient than $P$. The number of days it takes for $Q$ to do the same piece of work is

$2$ men alone or $3$ women alone can complete a piece of work in $4$ days. In how many days can $1$ woman and $1$ man together complete the same piece of work?

Vedclass Test Series

Exam Paper Generator

Online Exam Module