8
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

Answer:   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.

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.

9 121
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).

7 310
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

Explanation:

(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

7 262
Q:

K can finish the work in 18 days and L can do the same work in 15 days. L worked for 10 days and left the job. In how many days, K alone can finish the remaining work ?

 A) 5.5 days B) 6 days C) 4.2 days D) 5 days

Explanation:

L's 10 days work = $\inline \fn_jvn \small \left ( \frac{1}{15}\times 10 \right )= \frac{2}{3}$
Remaining work = $\inline \fn_jvn \small \left ( 1-\frac{2}{3} \right )=\frac{1}{3}$
Now, $\inline \fn_jvn \small \frac{1}{18}$ work is done by K in one day
$\inline \fn_jvn \small \frac{1}{3}$ work is done by K in $\inline \fn_jvn \small \left ( 18\times \frac{1}{3} \right ) = 6 days$

4 189
Q:

Raghu can complete a work in 12days working 9 hours a day. Arun can complete the same work in 8 days working 11 hours a day. If both Raghu and Arun work together, working 12 hours a day, in how many days can they complete the work ?

A) $\inline \fn_jvn \small 3\tfrac{4}{49} days$    B) $\inline \fn_jvn \small 12\tfrac{4}{49} days$  C)  $\inline \fn_jvn \small 4\tfrac{3}{49} days$   D)  $\inline \fn_jvn \small 4\tfrac{12}{49} days$

 A) Option A B) Option B C) Option C D) Option D

Raghu can complete the work in (12$\fn_jvn&space;\small&space;\times$9)hrs = 108 hrs.
Arun can complete the work in (8$\fn_jvn&space;\small&space;\times$11)hrs = 88 hrs.
Raghu's 1 hrs work = $\inline \fn_jvn \small \frac{1}{108}$ and Arun's 1 hrs work = $\inline \fn_jvn \small \frac{1}{88}$
(Raghu + Arun)'s 1 hrs work = $\inline \fn_jvn \small \left ( \frac{1}{108}+\frac{1}{88} \right ) = \frac{49}{2376}$
So, both Raghu and Arun will finish the work in $\inline \fn_jvn \small \left ( \frac{2376}{49}\right ) hrs$
Number of days of 12 hours each=$\inline \fn_jvn \small \left ( \frac{2376}{49}\times \frac{1}{12} \right )$ = $\inline \fn_jvn \small \frac{198}{49} = (4\tfrac{3}{49}) days$.