# Time and Work

Pratice Time and Work Questions and answers.

Rule Description
1

If A can do a piece of work in X days, then A’s one day’s work = $\frac{1}{X}$th part of whole work.

2

If A’s one day’s work = $\frac{1}{X}$th part of whole work, then A can finish the work in X days.

3

If A can do a piece of work in X days and B can do it in Y days then A and B working together will do the same work in $\frac{XY}{X+Y}$ days.

4

If A, B and C can do a work in X, Y and Z days respectively then all of them working together can finish the work in

$\frac{XYZ}{XY+YZ+ZX}$ days.

5

If (A + B) can do a piece of work in X days, (B + C) can do a place of work in Y days and (C + A) can do a piece of work in Z days.

Then, (A + B + C) can do a piece of work in

$\frac{2XYZ}{XY+YZ+ZX}$ days.

6

If A and B together can do a piece of work in X days and A alone can do it in Y days, then B alone can do the work in

$\frac{XY}{Y-X}$ days.

7

If (A + B + C) can do a piece of work in X days and (B + C) can do a piece of work in Y days, then

A can do a piece of work in

$\frac{XY}{Y-X}$ days.

8

A and B can do a work in ‘X’ and ‘Y’ days respectively. They started the work together but A left ‘a’ days before completion of the work. Then,

time taken to finish the work is

$\frac{Y(X+a)}{X+Y}$

9

If ‘A’ is ‘a’ times efficient than B and A can finish a work in X days, then working together,

they can finish the work in

$\frac{aX}{a+1}$ days

10

If A is ‘a’ times efficient than B and working together they finish awork in Z days then,

• time taken by A = $\frac{Z(a+1)}{a}$ days.
• time taken by B = $Z(a+1)$ days.
11

If A working alone takes ‘x’ days more than A and B together, and B working along takes ‘y’ days more than A and B together, then

number of days taken by A and B working together is given by $\sqrt{xy}$ days.

12

If a1 men and b1 boys can complete a work in x days, while a2 men and b2 boys can complete the same work in y days, then

$\frac{\text{One day work of 1 man}}{\text{One day work of 1 boy}}=\frac{\left(yb_2-xb_1\right)}{\left(xa_1-ya_2\right)}$

13

If n men or m women can do a piece of work in X days, then N men and M women together can finish the work in $\frac{nmX}{nM+mN}$ days.

14

A and B do a piece of work in a and b days, respectively. Both begin together but after some days, A leaves off and the remaining work is completed by B in x days. Then,

the time after which A left, is given by

$T=\frac{(b-x)a}{a+b}$

15

If ‘M1’ persons can do ‘W1’ works in ‘D1’ days and ‘M2’persons can do ‘W2’ works in ‘D2’ days then

M1D1W2 = M2D2W1

If T1 and T2 are the working hours for the two groups then

M1D1W2T1 = M2D2W1T2

Similarly,

M1D1W2T1E1 = M2D2W1T2E2,

where E1 and E2 are the efficiencies of the two groups.

16

If the number of men to do a job is changed in the ratio a : b, then the time required to do the work will be in the ratio b : a, assuming the amount of work done by each of them in the given time is the same, or they are identical.

17

A is K times as good a worker as B and takes X days less than B to finish the work. Then

the amount of time required by A and B working together is

$\frac{K \times X}{K^2 - 1}$ days.

18

If A is n times as efficient as B, i.e. A has n times as much capacity to do work as B, then A will take $\frac{1}{n}$ of the time taken by B to do the same amount of work.