3
Q:

A and  B can do  a piece of work in 30 days , while  B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish  the work?

 A) 18 days B) 24 days C) 30 days D) 36 days

Explanation:

2(A+B+C)'s 1 day work = $\inline&space;{\color{Black}\left&space;(&space;\frac{1}{30}+\frac{1}{24}+\frac{1}{20}&space;\right&space;)=\frac{15}{120}=\frac{1}{8}&space;}$

=>(A+B+C)'s  1 day's work=$\inline&space;{\color{Black}\frac{1}{16}&space;}$

work done by A,B and C in 10 days=$\inline&space;{\color{Black}\frac{10}{16}=&space;\frac{5}{8}}$

Remaining work=$\inline&space;{\color{Black}(1-\frac{5}{8})=&space;\frac{3}{8}}$

A's 1 day's work =$\inline&space;{\color{Black}(\frac{1}{16}-\frac{1}{24})=\frac{1}{48}}$

Now, $\inline&space;{\color{Black}\frac{1}{48}}$ work is done by A in 1 day.

So, $\inline&space;{\color{Black}\frac{3}{8}}$ work  wil be done by A in $\inline&space;{\color{Black}(48\times&space;\frac{3}{8})}$ = 18 days

Q:

P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share of R ?

 A) 120 B) 240 C) 360 D) 180

Explanation:

1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)
so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1
so R share = (1/10)x1200 = 120.

2 9
Q:

A group of men can complete a job in K hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of K ?

 A) 7 hrs B) 7.5 hrs C) 8 hrs D) 8.25 hrs

Explanation:

Let there are L men

job requires LK man hours.

job completed in first 4 hrs = Lx4 = 4L
job completed in next 4 hrs = 4xL/2 = 2L
job completed in next 4 hrs = 4xL/4 = L
job completed in last 4 hrs = 4xL/8 = L/2
4L + 2L + L + L/2 = KL
K = 7+1/2 = 7.5 hours.

2 13
Q:

A can do a work in 9 days, B can do a work in 7 days, C can do a work in 5 days. A works on the first day, B works on the second day and C on the third day respectively that is they work on alternate days. When will they finish the work ?

 A) [7 + (215/345)] days B) [6 + (11/215)] days C) [6 + (261/315)] days D) [5 + (112/351)] days

Explanation:

After day 1, A finishes 1/9 of the work.

After day 2, B finishes 1/7 more of the total work. (1/9) + (1/7) is finished.

After day 3, C finishes 1/5 more of total work. Total finished is 143/315.

So, after day 6, total work finished is 286/315.

Now remaining work = 315 - 286 = 29 /315

On day 7, A will work again

Work will be completed on day 7 when A is working. He must finish 29/315 of total remaining work.

Since he takes 9 days to finish the total task, he will need 261/315 of the day.

Total days required is 6 + (261/315) days.

3 28
Q:

One girl can eat 112 chocolates in half a minute, and her boy friend can eat half as many in twice the length of time. How many chocolates can both boy and girl eat in 12 seconds ?

 A) 44 B) 32 C) 56 D) 49

Explanation:

Girl eats 112 chocolates in 30 sec
so she can eat in 12 sec is 12 x 112/30 = 44.8 chocolates.

Her boy friend can eat one-half of 112 in twice of 30 sec
so he can eat 56 in 60 sec
Then he can eat in 12 sec is 56 x 12/60 = 11.2 chocolates.

Hence, together they can eat
=> 44.8 + 11.2
56 chocolates in 12 seconds.

5 21
Q:

Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$a week, what should be the wages of the girl a week ?  A) 24$ B) 22 $C) 16$ D) 14 $Answer & Explanation Answer: C) 16$

Explanation:

Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $28/week, so a girl will be paid 28x $\inline \fn_jvn \frac{\frac{2}{45}}{\frac{7}{90}}$ = 16$.