7
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:

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

Explanation:

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=$\inline \fn_jvn \small \left ( \frac{2376}{49}\times \frac{1}{12} \right )$ = $\inline \fn_jvn \small \frac{198}{49} = (4\tfrac{3}{49}) days$.

4 84
Q:

P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?

 A) 3 am B) 12 pm C) 1 pm D) 3 pm

Explanation:

Work done by P and Q in the first two hours, working alternately
= First hour P + Second hour Q
$\inline \fn_jvn \small \Rightarrow \frac{1}{4}+\frac{1}{12}=\frac{1}{3}$  work is completed in 2 hours
Then, the total time required to complete the work by P and Q working alternately=2$\fn_jvn&space;\small&space;\times$3=6hours
Thus, work will be completed at 3pm.

4 44
Q:

K is 4 times as fast as L and working together, they can complete a work in 24 days. In how many days can L alone complete the work ?

 A) 30 days B) 40 days C) 120 days D) 80 days

Explanation:

Given K=4L
$\Rightarrow$ K+L = 4L+L = 5L
These 5L people can complete the work in 24 days, which means L alone can do the work in

$\fn_jvn&space;\small&space;\Rightarrow$24$\times$5=120 days.

Hence, K alone can do the work in $\inline \frac{120}{4}$ = 30 days.

3 39
Q:

A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

 A) 11 days B) 12 days C) 13 days D) 14 days

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

18 4834
Q:

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?

 A) 4 days B) 5 days C) 6 days D) 7 days