Numerical Applications Test 26

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Numerical Applications Test 26

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Question 1
1 / -0

A water tank is $$\displaystyle\frac{2}{5}$$th full. Pipe $$A$$ can fill the tank in 10 minutes and pipe $$B$$ can empty it in $$6$$ minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

A
$$6$$ minutes to empty

B
$$6$$ minutes to fill

C
$$9$$ minutes to empty

D
$$9$$ minutes to fill

Solution

Pipe $$A$$ in 1 minute fills $$\displaystyle\frac { 1 }{ 10 }$$ part and pipe $$B$$ in 1 minute empties $$\displaystyle\frac { 1 }{ 6 }$$ part.
$$\therefore$$ Work done by pipe $$\left( A+B \right)$$ in 1 min $$ = \displaystyle\frac { 1 }{ 10 } - \displaystyle\frac { 1 }{ 6 } = \displaystyle\frac { 1 }{ 15 }$$
$$\Rightarrow \displaystyle\frac { 1 }{ 15 }$$ parts gets emptied in 1 min
$$\Rightarrow \displaystyle\frac { 2 }{ 5 }$$ part is emptied in $$15 \times \displaystyle\frac { 2 }{ 5 }$$ min $$ = 6$$ min.
Question 2
1 / -0

$$A$$ can do a work in $$15$$ days and $$B$$ in $$20$$ days. If they work on it together for $$4$$ days, then the fraction of the work that is left is:

A
$$\displaystyle \frac{1}{4}$$

B
$$\displaystyle \frac{1}{10}$$

C
$$\displaystyle \frac{7}{15}$$

D
$$\displaystyle \frac{8}{15}$$

Solution

$$ {\textbf{Step -1: Find the work left after 4 days.}} $$

$$ {\text{Let, total work = 1}} $$
$$ {\text{A can do the work in 15 days}} $$
$$ {\text{Amount of work A can do in 1 day = }}\dfrac{1}{{15}} $$
$$ {\text{B can do the work in 20 days}} $$
$$ {\text{Amount of work B can do in 1 day = }}\dfrac{1}{{20}} $$
$$ {\text{Amount of work done by A and B together in 1 day = }}\dfrac{1}{{15}} + \dfrac{1}{{20}} = \dfrac{7}{{60}} $$

$$ {\text{Amount of work A and B together can do in 4 days = 4}} \times \dfrac{7}{{60}} = \dfrac{7}{{15}} $$

$$ {\text{Work left after 4 days = } 1 - }\dfrac{7}{{15}} $$
$$ = \dfrac{8}{{15}} $$

$$ {\textbf{Hence, the correct option is D.}} $$
Question 3
1 / -0

Two workers A and B working together completed a job in $$ 5$$ days. If A worked twice as efficiently as he actually did and B worked $$\displaystyle \frac{1}{3}$$ as efficiently as he actually did the work would have been completed in $$3$$ days. A alone could complete the work in

A
$$\displaystyle 5\frac{1}{4}$$ days

B
$$\displaystyle 6\frac{1}{4}$$ days

C
$$\displaystyle 7\frac{1}{2}$$ days

D
None of these

Solution

Let the total work be $$W$$.
Let the speed of $$A$$ be $$x$$ work/day.
Let the speed of $$B$$ be $$y$$ work/day.
Two workers $$A$$ and $$B$$ working together completed a job in $$5$$ days.
$$\therefore \, \, \dfrac{W}{x+y}=5$$$$\therefore\,\,W=5x+5y$$ ..........(1)
If $$A$$ worked twice as efficiently as he actually did and $$B$$ worked $$\dfrac{1}{3}$$ as efficiently as he actually did the work would have been completed in $$3$$ day.
$$\therefore\,\,\dfrac{W}{2x+\dfrac{1}{3}y}=3$$
$$\therefore\,\,5W=30x+5y$$ .........(2)
Solving (1) and (2), we get
$$\dfrac{W}{x}=\dfrac{25}{4}$$
$$\therefore$$ $$A$$ alone could complete the work in $$\dfrac{25}{4}=6\dfrac{1}{4}$$ days.
Question 4
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$$A$$ alone can do a piece of work in $$6$$ days and $$B$$ alone in $$8$$ days. $$A$$ and $$B$$ undertook to do it for $$Rs. 3200.$$ With the help of $$C,$$ they completed the work in $$3$$ days. How much is to be paid to $$C$$?

A
$$300$$

B
$$400$$

C
$$600$$

D
$$800$$

Solution

C's 1 day's work $$= $$$$\dfrac{1}{3}-(\dfrac{1}{6}+\dfrac{1}{8})=\dfrac{1}{3}-\dfrac{7}{24}=\dfrac{1}{24}$$

A's wages : B's wages : C's wages$$ =\dfrac{1}{6}:\dfrac{1}{8}:\dfrac{1}{24}=4:3:1$$

$$\therefore$$ C's share (for 3 days)$$=Rs.\, (3 \times \dfrac{1}{24} \times 3200)=Rs.\, 400$$
Question 5
1 / -0

Ravi and Kumar are working on an assignment. Ravi takes $$6$$ hours to type $$32$$ pages on a computer, while Kumar takes $$5$$ hours to type $$40$$ pages. How much time will they take, working together on two different computers to type an assignment of $$110$$ pages?

A
$$20$$ hours

B
$$5$$ hours $$40$$ minutes

C
$$8$$ hours $$15$$ minutes

D
$$23$$ hours

Solution

Number of pages typed by Ravi in 1 hour$$=\dfrac{32}{6}=\dfrac{16}{3}$$

Number of pages typed by Kumar in 1 hour$$=\dfrac{40}{5}=8$$

Number of pages typed by both in 1 hour$$=(\dfrac{16}{3}+8)=\dfrac{40}{3}.$$

$$\therefore$$ Time taken by both to type 110 pages$$=(110 \times\, \dfrac{3}{40})\, $$hours.
$$=8\dfrac{1}{4}$$ hours (or) 8 hours 15 minutes..
Question 6
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$$A$$ and $$B$$ together can do a piece of work in $$30$$ days. $$A$$ having worked for $$16$$ days, $$B$$ finishes the remaining work alone in $$44$$ days. In how many days shall $$B$$ finish the whole work alone?

A
$$30$$ days

B
$$40$$ days

C
$$60$$ days

D
$$70$$ days

Solution

$$Let \, \,the \, \,total \, \, work \, \, be \, \, W.$$
$$Let \, \, the \, \, speed \, \, of \, \, A \, \, in \, \, doing \, \, entire \, \, work \, \, be \, \, x \, \, work/day$$
$$Let \, \, the \, \, speed \, \, of \, \, B \, \, in \, \, doing \, \, entire \, \, work \, \, be \, \, y \, \, work/day$$

$$\therefore \, \, \dfrac{W}{x+y}=30$$

$$\therefore$$ $$\, \, W=30x+30y............(1)$$

$$Work \, \, done \, \,by \, \,A \, \,in \, \,16 \, \,days \, \,=16x$$
$$Remaining \, \,work \, \,done \, \,by \, \,B \, \,in \, \,44 \, \,days=44y$$
$$\therefore \, \, 16x+44y=W.........(2)$$
$$From \, \,(1) \, \,and \, \,(2) \, \, ,W=60y$$
$$Hence, \, \,if \, \,B \, \,works \, \,alone \, \,then \, \,the \, \,work \, \,will \, \,be \, \,completed \, \,in \, \,\dfrac{W}{y} \, \,days \, \,= \, \,\dfrac{60y}{y} \, \,days \, \,=60 \, \,days.$$
Question 7
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A man a woman and a boy can complete a job in $$3, 4$$ and $$12$$ days respectively. How many boys must assist 1 man and 1 woman to complete the job in $$\displaystyle \frac{1}{4}$$ of a day?

A
$$1$$

B
$$4$$

C
$$19$$

D
$$41$$

Solution

($$1$$ man $$+$$ $$1$$ woman)'s $$1$$ day's work$$=\left (\dfrac{1}{3}+\dfrac{1}{4}\right)=\dfrac{7}{12}.$$
Work done by $$1$$ man and $$1$$ woman in $$\dfrac{1}{4}$$ day$$=\left (\dfrac{7}{12} \times \dfrac{1}{4}\right)=\dfrac{7}{48}$$
Remaining work $$=\left (1-\dfrac{7}{48}\right)=\dfrac{41}{48}$$
Work done by $$1$$ boy in $$\dfrac{1}{4}$$ day$$=\left (\dfrac{1}{12} \times \dfrac{1}{4}\right)$$$$=\dfrac{1}{48}$$
$$\therefore$$ Number of boys required $$=\left (\dfrac{41}{48} \times 48\right)=41$$.
Question 8
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$$24$$ men can complete a work in $$16$$ days, $$32$$ women can complete the same work in $$24$$ days. $$16$$ men and $$16$$ women started working and worked for $$12$$ days. How many more men are to be added to complete the remaining work in $$2$$ days?

A
$$16$$

B
$$24$$

C
$$36$$

D
$$48$$

Solution

24 men can complete the work in 16 days
1 man can complete the work in $$=16\times 24=384 Days$$
32 women cam complete the work in 24 days
1 woman can complete the work in a$$=32\times 24=768 days$$
Ratio between man and woman$$=384:768=1:2$$
then 1 man =2 women
The work is done br 16 men and 16 women in 12 days
16 women=8 men
thus the number of men complete the work in 12 days=$$16+8=24 men$$
Since 24 men takes 16 days to complete the work
So after 12 days,4 days work will be left for 24 Men
Thus the work left can be completed in 2 days by$$=24\times \dfrac{4}{2}=48 Days$$
Additional men required to complete the work in 2 days$$=48-24=24 men$$
Question 9
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$$12$$ men can complete a piece of work in $$4$$ days while $$15$$ women can complete the same work in $$4$$ days $$6$$ men start working on the job and after working for $$2$$ days all of them stopped working. How many women should be put on the job to complete the remaining work if it is to be completed in $$3$$ days ?

A
$$15$$

B
$$18$$

C
$$22$$

D
None of these

Solution

$$12$$ men can complete a piece of work in $$4$$ days
$$15$$ women can complete the same work in $$4$$ days
Let the productivity of men be $$m$$ and the productivity of women be $$w$$
Thus,
$$12m \times 4 = 15w \times 4$$
$$=>4m=5w$$
$$=>m=\displaystyle \frac{5}{4}w$$

Total work done by women $$=60w$$
Work done by 6 men in 2 days $$=6m \times 2$$
$$=6 \times \displaystyle \frac {5}{4} \times 2$$
$$=15w$$
Thus, remaining work $$=60w-15w$$
$$=45w$$
Let F women complete the remaining job in 3 days
Thus, $$Fw \times 3 = 45w$$

$$=>F=\displaystyle \frac{45}{3}$$

$$=>F=15$$
Thus, $$15$$ women are required to complete the job.
Question 10
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$$A$$ and $$B$$ together can do a piece of work in $$12$$ days which $$B$$ and $$C$$ together can do in $$16$$ days. After $$A$$ has been working at it for $$5$$ days and $$B$$ for $$7$$ days, $$C$$ finishes it in $$13$$ days. In how many days $$C$$ alone will do the work ?

A
$$16$$ days

B
$$24$$ days

C
$$36$$ days

D
$$48$$ days

Solution

Work done by (A+B)'s in 1 day$$=\dfrac{1}{12}$$
work done by (B+C)'s in 1 day$$=\dfrac{1}{16}$$
Let C does a work in x days
Then work done by C in a day$$=\dfrac{1}{x}$$
According to the questio
A's 5 day's work+B's 7 day's work+C's 13 day's work=1
(A+B)'s 5 day's+(B+C)'s 2 days+C's 11 day's
$$\dfrac{5}{12}+\dfrac{2}{16}+\dfrac{11}{x}=1$$
$$\dfrac{11}{x}=1-\dfrac{5}{12}-\dfrac{2}{16}$$
$$\dfrac{11}{x}=\dfrac{22}{48}$$
$$x=24 days$$

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Numerical Applications Test 26

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Numerical Applications Test 26

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SHARING IS CARING

Question 1

$$6$$ minutes to empty

$$6$$ minutes to fill

$$9$$ minutes to empty

$$9$$ minutes to fill

Solution

Question 2

$$\displaystyle \frac{1}{4}$$

$$\displaystyle \frac{1}{10}$$

$$\displaystyle \frac{7}{15}$$

$$\displaystyle \frac{8}{15}$$

Solution

Question 3

$$\displaystyle 5\frac{1}{4}$$ days

$$\displaystyle 6\frac{1}{4}$$ days

$$\displaystyle 7\frac{1}{2}$$ days

None of these

Solution

Question 4

$$300$$

$$400$$

$$600$$

$$800$$

Solution

Question 5

$$20$$ hours

$$5$$ hours $$40$$ minutes

$$8$$ hours $$15$$ minutes

$$23$$ hours

Solution

Question 6

$$30$$ days

$$40$$ days

$$60$$ days

$$70$$ days

Solution

Question 7

$$1$$

$$4$$

$$19$$

$$41$$

Solution

Question 8

$$16$$

$$24$$

$$36$$

$$48$$

Solution

Question 9

$$15$$

$$18$$

$$22$$

None of these

Solution

Question 10

$$16$$ days

$$24$$ days

$$36$$ days

$$48$$ days

Solution

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