Free Practice Questions for Time-and-work in Maths

ATQ,
B worked for last 5 days, so work done by $B=15$
Remaining work $=120-15=105$
Work done by both $\mathrm{A}$ and $\mathrm{B}=\frac{105}{7} =15$ days
So $\mathrm{A}$ work for 15 days.

Efficiency of Arti and Rita $=5$ units $/ \mathrm{h}$
If Efficiency of Arti = 4 units/h

 then Efficiency of Rita $=1$ unit $/ \mathrm{h}$
Total Work $=40$ units
So, time taken by Rita to do the job $=\frac{40}{1}$ h $=40$ h

According to question

$A \times 40 = A \times 10 + B \times 45$
$A \times 30=B \times 45$
$\frac{A}{B}=\frac{3}{2}$
Total work $=A \times 40=3 \times 40=120$
$75 \%$ of $120=\frac{3}{4} \times 120=90$
Time $=\frac{90}{(3+2)}=\frac{90}{5}=18$ days

Let the efficiency of John be J and that of Manu be M.

Work done by John = Work done by Manu, So

$J \times 8 \times 6=M \times 3 \times 4$
$\frac{J}{M}=\frac{12}{48}=\frac{1}{4}$, per hour

Total work = $1\times 8 \times 6$ =48 unit

John and Manu complete (1+4)=5 unit in an hour

So, John and Manu's one day's work $=5 \times \frac{48}{5}=48$ unit
Time taken by both to complete the whole work working $9 \frac{3}{5}$ hours daily $=\frac{48}{48}=1$ day

Let the total work be 30, (LCM of 10 & 15), So
Efficiency of $\mathrm{A}=\frac{30}{10}=3$
Efficiency of $\mathrm{B}=\frac{30}{15}=2$
Let the project completed in t days, then
3t+2(t-5)=30
3t+2t-10=30
5t=40
t=8 days

Let A complete the remaining work in x days.

The efficiency of A is 1/40

And the efficiency of B is 1/50

So, the efficiency of A and B together is

⇒ (1/40) + (1/50)

⇒ (5 + 4)/200 = 9/200

A and B worked for 5 days, rest completed by A

⇒ (9/200) × 5 + (1/40) × x = 1

⇒ 9/40 + x/40 = 1

⇒ 9 + x = 40

⇒ x = 31 days

∴ A will complete the rest of the work in 31 days.

Alternate Method

The total efficiency of A and B is

⇒ 5 + 4 = 9

They worked for 5 days

⇒ 9 × 5 = 45

Rest of the work completed by A

⇒ (200 - 45)/5 = 31 days.

∴ A will complete the rest of the work in 31 days.

Let efficiency of A's and B is 5x and x

According to the question,

B-A=52 days 

5x-1x=52 days 

4x =52 days 

x=13 days 

So, Total work =13×5=65

A and B complete the work together in $=  \frac{65}{6} = 10 \frac{5}{6}$

A can do a piece of work in 45 days.

A's 1 days work =1/45

A's 30 days work =1/45×30=2/3

The remaining work =1-2/3=1/3

B's complete 1/3 th of work in 5 days

Then, B's 1 day work =1/(3×5)=1/15

B can complete the whole work =15 days

Let total work $= 60$ unit

Efficiency of A $= \frac{60}{10}=6$

Efficiency of B $= \frac{60}{12}=5$

Efficiency of C $= \frac{60}{15}=4$

On the first day, B is assisted by A and on the Second day, B is assisted by C and this continues

So in two days $(6+5) + (5+4) = 20$ units of work get completed.

To complete 60 units of work, It will take $2\times3 = 6$ days

Let the efficiency of men is $M$ and that of boys is $B$, then
$
(5 M+2 B) \times 30=(7 M+10 B) \times 15
$
$150 M+60 B=105 M+150 B$
$45 M=90 B$
$\frac{M}{B}=\frac{2}{1}$
Total work $=30 \times(5 \times 2+2 \times 1)=30 \times 12=360$
Let the work is now completed by $x$ boys and 40 men in 4 days
So, $\frac{360}{40 \times 2+x}=4$
$
\begin{aligned}
&80+x=90 \\
&x=10
\end{aligned}
$

$A$ completes $25 \%$ of the total work in 15 days, so
Time taken to complete whole work $=\frac{15}{25} \times 100=60$ days
$\mathrm{B}$ completes $75 \%$ of the total work in 30 days, So
Time taken to complete whole work $=\frac{30}{75} \times 100=40$ days
Let the total work be $120,(\mathrm{LCM}$ of 60 and 40$)$
Efficiency of $\mathrm{A}=\frac{120}{60}=2$
Efficiency of $\mathrm{B}=\frac{120}{40}=3$
So, time taken to complete $50 \%$ of total work $=\frac{50}{100} \times \frac{120}{(2+3)}=\frac{1}{2} \times \frac{120}{5}=12$ days

Let the total work be 120 . (LCM of 8,10 and 12 )
Efficiency of $\mathrm{A}=\frac{120}{8}=15$
Efficiency of $\mathrm{B}=\frac{120}{10}=12$
Efficiency of $\mathrm{C}=\frac{120}{12}=10$
They worked together, So
Ratio of efficiencies $=$ Ratio of wages
Total wages $=15+12+10=37$ unit
Given that
$37 \rightarrow $₹ 5550
$1 \rightarrow $₹ 150
So, Share of B
$12 \rightarrow $₹ 1800

Let the total work be 240 , (LCM of 48 and 60), So
Efficiency of $\mathrm{A}=\frac{240}{48}=5$
Efficiency of $\mathrm{B}=\frac{240}{60}=4$
They worked for 12 days
So, Work completed in 12 days $=12 \times(5+4)=108$
Remaining work $=240-108=132$
So, $25 \%$ of 132 work is to be completed by B
Time $=\frac{25}{100} \times \frac{132}{4}=\frac{33}{4}=8 \frac{1}{4}$ days
Or 8 days $\frac{1}{4} \times 24 h r=8$ days 6 hours

$66 \frac{2}{3} \%$ of work is done by $B$ in 30 days.
$\Rightarrow$ Complete work will be done by $B$ in $\frac{30 \times 3}{2}=45$ days ( as 66 $\frac{2}{3} \%=\frac{2}{3}$ )
Now, Let the total work be $\operatorname{LCM}(25,45)=225$ units
According to question,
Efficiency of $(A+B)=\frac{225}{25}=9$
And, efficiency of $B=\frac{225}{45}=5$
So, efficiency of $A=9-5=4$
$\Rightarrow A$ will do $\frac{4}{15}$ part of the work in $=\frac{\frac{4}{15} \times 225}{4}=15$ days

A Let total work be $\operatorname{LCM}(36,60,45)=180$
So, combined efficiency of $A$ and $B=\frac{360}{36}=10$
Also, combined efficiency of $B$ and $C=\frac{360}{60}=6$
And, combined efficiency of $A$ and $C=\frac{360}{45}=8$
$\Rightarrow$ Combined efficiency of $A, B$ and $C=\frac{10+6+8}{2}=12$
$\Rightarrow$ Efficiency of $B=12-8=4$
So, required time $=\frac{360}{4}=90$ days

Let total work be LCM10,5 $=10$
$\Rightarrow$ Efficiency of $A=1010=1$
$\Rightarrow$ Efficiency of $B=105=2$
Now, work done by A and B together in 2 days $=2 \times 1+2=6$
$\Rightarrow$ Work done by A and $\mathrm{C}$ in 3 days $=10-6=4$
$\Rightarrow$ Efficiency of $\mathrm{C}=4-1 \times 33=13$
So, time taken by $\mathrm{C}$ alone to complete $60 \%$ of the work $=0.6 \times 1013=18$ days

Let the efficiency of $A$ be 2 , then efficiency of $B=1$
Now, total work
So, time taken by B alone to complete the workdays

Let the total work be $92,(\mathrm{LCM}$ of 46,92 and 23 )
So, Efficiency of $\mathrm{X}=\frac{92}{46}=2$
Efficiency of $\mathrm{Y}=\frac{92}{92}=1$
And Efficiency of $\mathrm{Z}=\frac{92}{23}=4$
Let the total time taken by $\mathrm{X}$ to complete the whole work be t, then
$2 \times t+1 \times(t-2)+4 \times(t-8)=92$
$2 t+t-2+4 t-32=92$
$7 t=126$
$t=18 \mathrm{hr}$

3 पुरुषों का 1 दिन का काम
$=6$ स्त्रियों का 1 दिन का काम
1 पुरुष का 1 दिन का काम
$=2$ स्त्रियों का 1 दिन का काम
12 पुरुषों व 8 स्त्रियों का 1 दिन का काम
$=32$ स्त्रियों का 1 दिन का काम

$32: 6:: 16: x$
$x=\frac{6 \times 16}{32}=3$ दिन