Time and Work Quiz-1

Rajesh can build the wall in 20 days

1 day = 1/20 of the wall

Suresh can build the wall in 15 days

1 day = 1/15 of the wall

together they can build the wall in

1/20+1/15 days

= 7/60

Hence they together can complete the wall in 60/7=8.5 days

P and Q can complete the task in 12 days.

So in 1 day, the amount of work done by them= 1/12

P and R can complete the task in 10 days

So in 1 day, the amount of work done by them= 1/10

Q and R can complete the task in 18 days

So in 1 day, the amount of work done by them= 1/18

Adding all there work=

2 (P + Q + R) = 1/12 + 1/10 + 1/18= 43/180

2 (P + Q + R) = 43/180

(P + Q + R) = 43/360

Hence they will complete the work in 360/43 days

 

Let the two friends be x and y where x is slower than y

x can complete the task in 12 days

one day work will be 1/12

y is twice as fast of x

so y will take 12/2 days

one day work by y = 1/6

total number of days taken by them both(working together) to complete the job = 1/12 + 1/6= 3/12 = 1/4

Hence 4 days

Let ashish remove x number of men.

So he needs 24-x men to complete the remaining work

Let

Men= M, Days=D, Time/hours = T, Work = W

M1D1T1W2 = M2D2T2W1

Note that W2 is on left side and W1 is on right side

M1 = 24, D1 = 6, W1 = 80% of 1 = 0.8

M2 = 24-x, D2 =  4, W2 = 20% of 1 = 0.2

(24 x 6 x 0.2) = (24-X x 4 x 0.8 )

9 = x

raju is completing 25% of the work in 5 days he will complete 100% of the work in

(100/25) x 5 = 20 days

If raju can complete 100% of the work in 20 days then he will complete 10 times of the same work in 20 x 10 = 200 days.

Let the time taken to complete the work = x days

According to question,

(4 men + 3 women) x 6 = (5 men + 7 women) x 4

12 Men + 9 women = 10 Men + 14Women

2 Men = 5Women

4 Men = 10 Women

Again according to question,

(10 + 3)\times 6 = (\frac{5}{2}+1) \times x

78 = \frac{7}{2} \times x

x= 22(2/7) days

A can do the work in 10 days

In 1 day A will do 1/10 work

B can do the work in 20 days

In one day B will do 1/20 work

A+B+C can complete the work in 5 days

In one day they will do 1/5 work

now

A's work + B's work + C's work= total work

C's work = 1/5 - (1/10 + 1/20)

= 1/5 - (3/20)

= 1/20

hence 20 days

Work done by A in 5 days = 1/20*5 =1/4
Remaining work=(1-1/4) =3/4
Now, 3/4 work is done by B in 10 days
The whole work will be done by B in 10*4/3= 40/3 days
As 1 day's work of A = 1/20
1 day's work of B =3/40
(A+B)'s 1 day's work= 1/20+3/40 = 1/8
So, both finished the work in 8 days.

Raju being twice as good as workman as Vijay, you can solve the  following equation to get the required answer :

1/R + (1/2)R = 1/14

or, 3/R = 14

or, R = 42

Vijay alone can do the same work in 42 days.