(B) Let the efficiency of $A$ be $a$ and $B$ be $b$ units per day.Total work $= 5(a + b)$.According to the second condition,the work is completed in $

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

(B) Let the efficiency of $A$ be $a$ and $B$ be $b$ units per day.Total work $= 5(a + b)$.According to the second condition,the work is completed in $3$ days with efficiencies $2a$ and $\frac{b}{3}$.So,$3(2a + \frac{b}{3}) = 5(a + b)$.$6a + b = 5a + 5b$.$a = 4b$,which means $\frac{a}{b} = \frac{4}{1}$.Total work $= 5(4 + 1) = 25$ units.Time taken by $A$ alone $= \frac{\text{Total Work}}{\text{Efficiency of } A} = \frac{25}{4} = 6 \frac{1}{4}$ days.

Competitive Quantitative Aptitude Time and Work and Wages Time and Work

Medium

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).

A
$6 \frac{1}{2}$
B
$6 \frac{1}{4}$
C
$6 \frac{3}{4}$
D
$12 \frac{1}{2}$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Time and Work and Wages

Subtopic

Time and Work

$A, B$ and $C$ completed a work costing $Rs. 1800$. $A$ worked for $6$ days,$B$ for $4$ days and $C$ for $9$ days. If their daily wages are in the ratio of $5: 6: 4$,how much amount will be received by $A$ (in $Rs.$)?

Medium

View Solution

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?

Difficult

View Solution

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

Medium

View Solution

$A$ contract is to be completed in $50 \text{ days}$ and $105 \text{ men}$ were set to work,each working $8 \text{ hours a day}$. After $25 \text{ days}$,$\frac{2}{5}$ of the work is finished. How many additional men must be employed so that the work may be completed on time,with each man now working $9 \text{ hours a day}$?

Difficult

View Solution

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Two workers $A$ and $B$ working together completed a job in $5$ days. If $A$ worked twice as efficiently as he actually did and $B$ worked $\frac{1}{3}$ as efficiently as he actually did,the work would have completed in $3$ days. Find the time for $A$ to complete the job alone (in days).

Similar Questions

$A, B$ and $C$ completed a work costing $Rs. 1800$. $A$ worked for $6$ days,$B$ for $4$ days and $C$ for $9$ days. If their daily wages are in the ratio of $5: 6: 4$,how much amount will be received by $A$ (in $Rs.$)?

$A$ can complete a piece of work in $40$ days. He starts working,but having some other engagements,he leaves after $5$ days. Thereafter,$B$ completes the remaining work in $21$ days. How many days would $A$ and $B$ take to complete this work working together?

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

Vedclass Test Series

Exam Paper Generator

Online Exam Module