4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?

Correct Answer: 36

Explanation:

Given 4men, 12 women and 20 children work for  2 days.

Workdone for 2 days by 4men, 12 women and 20 children =  4 x 2 6 x 12 + 12 x 2 8 x 18 + 20 x 2 18 x 10 = 1 2

Therefore, remaining work = 1 -  1 2 =  1 2

To complete the same work by only men in 1 day,

We know that M1 x D1 = M2 x D2

Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1

12 x 6 = M x 1

=> M = 12 x 6 = 72

=> But the remaining work = 1/2

Men required => 1/2 x 72 = 36

Only men required to Complete the remaining work in 1 day = 36.

 

Correct Answer: 4 days

Explanation:

Given 10 men take 15 days to complete a work

=> Total mandays = 15 x 10 = 150

Let the work be 150 mandays.

=> Now 37 men can do 150 mandays in 150/37 =~ 4 days

Correct Answer: 26.6 days

Explanation:

Arun has completed 1 3rd of the work in 8 days

Then he can complete the total work in

1 3 ---- 8

 1 ---- ?

= 24 days

But given Akhil is only 60% as efficient as Arun

Akhil = 1 24 × 60 100 = 1 40

Akhil can complete the total work in 40 days

Now, remaining 2/3rd of work can be completed in

 1  ------   40

2 3 ------   ?  

= 26.66 days.

Correct Answer: 64 days

Explanation:

(P+Q)'s 1 day work = 1/24

P's 1 day work = 1/32

=> Q's 1 day work = 1/24 - 1/32 = 1/96

Work done by (P+Q) in 8 days = 8/24 = 1/3

Remainining work = 1 - 1/3 = 2/3

Time taken by Q to complete the remaining work = 2/3 x 96 = 64 days.

Correct Answer: 4 days

Explanation:

Given that 

6 men and 8 boys can do a piece of work in 10 days 

26 men and 48 boys can do the same in 2 days

 

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ??(1)

 

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

Correct Answer: 2.25 days

Explanation:

1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 x 6 = 2/3

Remaining work = 1 - 2/3 = 1/3

16 men's 1 day work = 1/108 x 16 = 4/27
4/27 work is done by them in 1 day.

1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

Correct Answer: 6 days

Explanation:

M = 10 days

The ratio of efficiency of M & N are 3 : 2

Hence, the time rquired for N alone = 15 days

=> Required time taken t=by both to complete the work = M x N / M + N 

= 10 x 15/ 10 + 15

= 150/25

= 6 days.

Correct Answer: 3:09 pm

Explanation:

Efficiency of P= 100/20= 5% per hour  

Efficiency of Q= 100/25= 4% per hour  

Efficiency of R= 100/40= 2.5% per hour  

Efficiency of S=100/50= 2% per hour 

 

Cistern filled till 10 am by P, Q and R  

Till 10 . 00 am Pipe P filled 20 % Till 10 . 00 am Pipe Q filled 8 % Till 10 . 00 am Pipe R filled 2 . 5 % 30 . 5 %  

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern. 

Rest of cistern to be filled = 100 - 30.5 = 69.5%  

 

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern 

= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).

Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins

 

It means cistern will be filled up at 3:09 pm

Correct Answer: 13 days

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

 

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

 

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in 13 days.

Correct Answer: 12 days

Explanation:

9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.