3
Q:

# Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when  working alone. Amit and Bharath both started the work together but Bharath  left after some days and Amit finished the remaining work in 56 days with half of his efficiency but he did the work with Bharath with his complete efficiency. For how many days they had worked together?

 A) 6 B) 8 C) 9 D) 12

Explanation:

$\inline \fn_jvn \begin{matrix} & Amit& Bharath\\ No.of\: days& 45& 40\\ Efficiency& 2.22\: percent\left ( =\frac{1}{45} \right ) &2.5 \: percent\left ( =\frac{1}{40} \right ) \end{matrix}$

Amit did the work in 56 days = $\inline \fn_jvn 56\times \frac{1}{45\times 2}=\frac{28}{45}$

$\inline \fn_jvn \therefore$ Rest work $\inline \fn_jvn \left ( \frac{17}{45} \right )$ was done by Amit and Bharath = $\inline \fn_jvn \frac{17/45}{17/360}$ = 8 days

( since Amit and Bharath  do the work in one day = $\inline \fn_jvn \frac{1}{45}+\frac{1}{40}=\frac{17}{360}$)

Q:

Adam and Smith are working on a project. Adam takes 6 hrs to type 36 pages on a computer, while Smith takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type a project of 120 pages?

 A) 8 hrs 45 min B) 8 hrs 42 min C) 8 hrs D) 8 hrs 34 min

Explanation:

Number of pages typed by Adam in 1 hour = $\inline \fn_jvn \small \frac{36}{6}$ = 6
Number of pages typed by Smith in 1 hour = $\inline \fn_jvn \small \frac{40}{5}$ = 8
Number of pages typed by both in 1 hour = (6 + 8) = 14
Time taken by both to type 110 pages = (120 * 1/14) = 8 $\inline \fn_jvn \small \frac{4}{7}$ = 8 hrs 34 min.

3 31
Q:

After working for 8 days, Arun finds that only $\inline \fn_jvn \small \frac{1}{3}$ rd of the work has been done. He employs Akhil who is 60% as efficient as Arun. How many days more would Akhil take to complete the work?

 A) 24.5 days B) 26.6 days C) 25 days D) 20 days

Explanation:

Arun has completed $\inline \fn_jvn \small \frac{1}{3}$ rd of the work in 8 days
Then he can complete the total work in
$\inline \fn_jvn \small \frac{1}{3}$ ---- 8
1 ---- ?
= 24 days
But given Akhil is only 60% as efficient as Arun
Akhil = $\inline \fn_jvn \small \frac{1}{24}\times \frac{60}{100}=\frac{1}{40}$
Akhil can complete the total work in 40 days
Now, remaining 2/3rd of work can be completed in
1 ------   40
$\inline \fn_jvn \small \frac{2}{3}$  ------   ?   $\fn_jvn&space;\small&space;\Rightarrow$ 26.66 days.

3 30
Q:

50 men can build a tank in 40days, but though they begin the work together, 5 men quit every ten days. The time needed to build the tank is ?

 A) 50 days B) 48 days C) 47.5 days D) 49 days

Explanation:

50 men can build a tank in 40 days
Assume 1 man does 1 unit of work in 1 day
Then the total work is 50×40 = 2000 units

50 men work in the first 10 days and completes 50×10 = 500 units of work
45 men work in the next 10 days and completes 45×10 = 450 units of work
40 men work in the next 10 days and completes 40×10 = 400 units of work
35 men work in the next 10 days and completes 35×10 = 350 units of work
So far 500 + 450 + 400 + 350 = 1700 units of work is completed and

remaining work is 2000 - 1700 = 300 units

30 men work in the next 10 days. In each day, they does 30 units of work.

Therefore, additional days required = $\inline \fn_jvn \small \frac{300}{30}=10$

Thus, total 10+10+10+10+10 = 50 days required.

4 18
Q:

In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?

 A) 10 days B) 15 days C) 20 days D) 5 days

Explanation:

After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days
$\fn_jvn&space;\small&space;\Rightarrow$ If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

6 87
Q:

Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?

 A) 4:5 B) 3:4 C) 4:3 D) 2:3

(20$\fn_jvn&space;\small&space;\times$18) men can complete the work in in one day.
one man's one day work = $\inline \fn_jvn \small \frac{1}{360}$
(18$\fn_jvn&space;\small&space;\times$15) women can complete the work in 1 day
1 woman's one day work = $\inline \fn_jvn \small \frac{1}{270}$
So, required ratio = $\inline \fn_jvn \small \frac{1}{270} :\frac{1}{360}$ = 4:3