# CAT2019-2: 71

249 views

Anil alone can do a job in $20$ days while Sunil alone can do it in $40$ days. Anil starts the job, and after $3$ days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done $10$% of the job, then in how many days was the job done?

1. $14$
2. $13$
3. $15$
4. $12$

edited

Given that, Anil alone can do a job in $20$ days, and Sunil alone can do a job in $40$ days.

• Anil $\rightarrow 20$ days
• Sunil $\rightarrow 40$ days

LCM of $20$ and $40 \Rightarrow 40\;\text{units}$ (Total work)

• Anil efficiency  $=\frac{40}{20} \Rightarrow 2$
• Sunil efficiency $= \frac{40}{40}\Rightarrow 1$

Work done by Anil in $3$ days $= 2 \times 3 = 6\;\text{units}$

Now, remaining work $= 40 – 6 = 34\;\text{unit}$

Let the number of days Anil and Sunil done the work together be $x$ days.

Bimal has done $10\%$ of the work $= 40 \times \frac{10}{100} = 4\;\text{units}$

Remaining  work done by Anil and Sunil $= 34-4=30\;\text{units}$

The number of days Anil and Sunil did the work together $x = \frac{30}{(2+1)} = \frac{30}{3} = 10$ days.

$\therefore$ The total time to complete the work $= x + 3 = 10 + 3 = 13$ days.

498 points 1 2 5
edited by

## Related questions

1
196 views
The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$, and in the ratio $3:4:3$ in $2015$. If Ramesh’s salary increased by $25$% during $2010-2015$, then the percentage increase in Rajesh’s salary during this period is closest to $8$ $7$ $9$ $10$
2
107 views
If x is a real number, then $\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$ is a real number if and only if $1\leq x\leq 2$ $-3\leq x\leq 3$ $1\leq x\leq 3$ $-1\leq x\leq 3$
In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$. The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$. Then Anjali's score exceeded Rama's score by $24$ $26$ $32$ $35$
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$?____
Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is $\sqrt{2}$ $\frac{\pi }{3}$ $\frac{1}{\sqrt{2}}$ $1$