WeCP Time and Work Quiz 1

Explanation :

Let the two conditioners be A and B

'A' cools at 30min

'B' at 45min

Together = \frac{(a \times b)}{(a + b)}

Together = \frac{(45 \times 30)}{(45 + 30)}

= \frac{45 \times 30}{75}

= 18.

Explanation :

Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work  x/4.

So,

\left ( \frac{5x}{2} + 7x + \frac{9x}{4} \right ) = \frac{1}{6}

\frac{47x}{4} = \frac{1}{6} \Rightarrow = \frac{2}{141} = 71 \text{ days }(approx)

1 woman alone can complete the work in 71 days.

So, to complete the work in 6 days, the number of women required = (71/6) = 12.

Correct is C

Explanation :

\frac{m \times T}{W} = constant

where, M= Men (no. of men)

T= Time taken

W= Work load

So, here we apply

\frac{M_{1} \times T_{1}}{W_{1}} = \frac{M_{2} \times T_{2}}{W_{2}}

Given that, M_{1} = 7 men, T_{1} = 12 hours ; T_{2} = 3 hours, we have to find M_{2} =?

Note that here, W_{1} = W_{2} = 1 road, ie. equal workload.

Clearly, substituting in the above equation we get, M_{2} = 28 men.

Explanation :

Let A's 1 day's work = x and B's 1 day's work = y

Then x+y = 1/50 and 25x+75y=1

25x + 75y = 1 ……..(1)

50x + 50y = 1 ……..(2)

1250x + 3750y = 50 ......(3)

1250x + 1250y = 25 .......(4)

Subtracting eq 4 from 3 we get

2500y = 25

y = \frac{1}{50}

Solving these two equations , we get : x= 1/50 and y= 1/50

Therefore B's  1 day work = 1/50

Hence,B alone shall finish the whole work in 50 days

Explanation :

Work done by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.

Thus, the total time required to complete the work  = 2 (3) = 6 days

Explanation :

A + B= 65

B + C =55

=>A+B+C = 100

So (A+B)+(B+C)-(A+B+C) = B

65+55-100  = B

B = 20

A = 45

C = 35

 

A is most efficient

Explanation :

(P+Q)'s 1 day work = 1/30

P's 1 day work = 1/40

=> Q's 1 day work = 1/30 - 1/40 = 1/12

Work done by (P+Q) in 6 days = 6 / 12 = 1/2

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

Time taken by Q to complete the remaining work = 1 / 2 x 12  = 6 days

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

 

Work done till 10 am by P,Q,R.

Till 10 am P has done 20%

Till 10 am Q has done 8%

Till 10 am R has done 2.5%

Thus till 10am P,Q and R has done 30.5% of work

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

Rest of work to be done = 100 - 30.5 = 69.5%

Now, the time taken by P,Q,R and S together to do the remaining work

= 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 work will be completed  at 3:09 pm

Explanation :

Given 5000 ---- 72 days

The provisions for men for 57 days can be completed by 'm' men for only 35 days.

i.e, 5000 ----- 57 days == m ---- 35 days

=> m x 35 = 5000 x 57

m = 8143

So total men for 35 days is 3900

=> 5000 old and 3143 new reinforcement.

Hence, reinforcement = 3143.

Explanation :

5M + 2B = 4(1M + 1B)

5M + 2B = 4M + 4B

1M = 2B

The required ratio of work done by a man and a boy = 2:1