Numerical Applications Test 49

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Numerical Applications Test 49

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Weekly Quiz Competition

Question 1
1 / -0

$$A, B$$ and $$C$$ complete a piece of work in $$25, 20$$ and $$24$$ days respectively. All work together for $$2$$ days and then $$A$$ and $$B$$ leave the work . $$C$$ works for next $$\displaystyle8\frac{3}{5}$$ days and then $$A$$ along with $$D$$ join $$C$$ and they all finish the work in next three days. In how many days $$D$$ alone can complete the whole work ?

A
$$22$$ days

B
$$\displaystyle21\frac{1}{2}$$days

C
$$23$$ days

D
$$\displaystyle22\frac{1}{2}$$days

Solution

Let the amount of work be $$x$$.

Now $$A$$ does the work in $$25$$ days.
$$\therefore $$ In $$1$$ day $$A$$ does $$\dfrac { x }{ 25 } $$ work,

$$B$$ does the work in $$20$$ days.
$$\therefore $$ In $$1$$ day $$B$$ does $$\dfrac { x }{ 20 } $$ work,

$$C$$ does the work in $$24$$ days.
$$\therefore $$ In $$1$$ day $$C$$ does $$\dfrac { x }{ 24 } $$ work.

$$A$$ works for $$(2+3)$$ days $$=5$$ days.
$$\therefore $$ In $$5$$ days $$A$$ does $$5\times \dfrac { x }{ 25 } $$ work $$=$$ $$\dfrac { x }{ 5 } $$ work,

$$B$$ works for $$2$$ days.
$$\therefore $$ In $$5$$ days $$B$$ does $$2\times \dfrac { x }{ 20 } $$ work=$$\dfrac { x}{ 10 } $$ and

$$C$$ works for $$\left( 2+8\dfrac { 3 }{ 5 } +3 \right) $$days=$$\dfrac { 68 }{ 5 } $$days.
$$\therefore $$ In $$\dfrac { 68 }{ 5 } $$ days $$C$$ does $$\dfrac { 68 }{ 5 } \times \dfrac { x }{ 24 } $$ work=$$\dfrac { 17x }{ 15 } $$ work.
$$\therefore $$ The total work done by $$A, B$$ and $$C$$, so far $$=$$ $$\dfrac { x }{ 5 } +\dfrac { x }{ 10 } +\dfrac { 17x }{ 13 }$$ work $$=$$ $$\dfrac { 13x }{ 15 } $$ work.
$$\therefore $$ The work left $$=$$ $$x-\dfrac { 13x }{ 15 } $$ work

This work is done by $$D$$ in $$3$$ days.
$$\therefore $$ $$D$$ will finish the whole i.e $$x$$ work in $$3\times \dfrac { 15 }{ 2 } $$days $$=$$$$22\dfrac { 1 }{ 2 } $$ days.

Ans- Option D.
Question 2
1 / -0

Two pipes can fill a tank in $$25$$ and $$30$$ minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in $$15$$ minutes. The capacity of the tank is:

A
$$ 120\ gallons $$

B
$$ 250 \ gallons $$

C
$$ 450 \ gallons $$

D
$$ 500 \ gallons $$

E
$$ 140 \ gallons $$

Solution

Water supplied by Pipe 1 be $$=\dfrac{V}{25}$$

Water supplied by Pipe 2 be $$=\dfrac{V}{30}$$

Water supplied when all pipes are working $$=\dfrac{V}{15}$$

So,
$$\Rightarrow \dfrac{V}{25}+\dfrac{V}{30}-3=\dfrac{V}{15}$$

$$\Rightarrow \dfrac{V}{25}+\dfrac{V}{30}-\dfrac{V}{15}=3$$

Solving we get
$$V=450$$ $$ gallons$$

therefore Answer is $$(C)$$
Question 3
1 / -0

A can complete a piece of work in $$18$$ days, B in $$20$$ days and C in $$30$$ days. B and C together start the work and forced to leave after $$ 2 $$ days. the time taken by A alone to complete the remaining work is

A
$$10$$

B
$$12$$

C
$$15$$

D
$$16$$

Solution

(B + C)'s 2 days work = 2 *(1/20 + 1/30) = 2 *(3 + 2 / 60) = 1/6 part
Remaining work = 1 - 1/6 = 5/6 part
A' s one day work = 1/18 part
Time taken to complete the work,
= (5/6) / (1/18) days; Hence, Time taken to complete the work
= (5/6) *18 = 15 days.
Question 4
1 / -0

$$A$$ can do a work in $$15$$ days and $$B$$ can do the same work in $$ 20$$ days, if $$A$$ and $$B$$ has done work for $$4$$ days together, the fraction of work left?

A
$$\dfrac{8}{15}$$

B
$$\dfrac{2}{15}$$

C
$$\dfrac{1}{5}$$

D
$$\dfrac{7}{13}$$

E
$$\dfrac{16}{15}$$

Solution

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

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

$$ {\text{Amount of work A and B together can do in 4 days = 4}} \times \dfrac{7}{{60}} = \dfrac{7}{{15}} $$
$$ {\text{Work left after 4 days = } 1 - }\dfrac{7}{{15}} $$
$$ = \dfrac{8}{{15}} $$

$$ {\textbf{Hence, the correct option is A.}} $$
Question 5
1 / -0

Two pipes can fill an empty tank separately in $$24$$ minutes and $$40$$ minutes respectively and a third pipe can empty $$30$$ gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is

A
$$500$$

B
$$550$$

C
$$600$$

D
$$700$$

Solution

Work done by two pipes individually is $$\dfrac{1}{24}$$ and $$\dfrac{1}{40}$$ respectively
work done by all three pipe together is $$\dfrac{1}{60}$$
Work done by third pipe to empty tha tank $$=\dfrac{1}{60} - (\dfrac{1}{24} + \dfrac{1}{40})$$
$$= \dfrac{1}{60} - \dfrac{8}{120}$$
$$= - \dfrac{1}{20}$$ [-ve sign means emptying]
$$\therefore$$ Volume of $$\dfrac{1}{20}$$ part $$= 30$$ gallons
$$\therefore$$ Volume of whole tank $$= 30 \times 20 = 600$$ gallons
Answer is $$600$$ gallons.
Question 6
1 / -0

A tap A can fill a cistern in $$8$$ hours while tap B can fill it in $$4$$ hours. In how much times will the cistern be filled if both A and B are opened together?

A
$$2hrs\;30min$$

B
$$2hrs\;40min$$

C
$$2hrs\;50min$$

D
$$3hrs$$

Solution

Time taken by tap A to fill the cistern $$=8$$ hours.
Work done by tap A in $$1$$ hour $$=\dfrac{1}{8}$$
Time taken by tap B to fill the cistern $$=4$$ hours.
Work done by tap B in $$1$$ hour $$=\dfrac{1}{4}$$
Work done by $$\begin{pmatrix}A+B\end{pmatrix}$$ in $$1$$ hour $$=\dfrac{1}{8}+\dfrac{1}{4}=\dfrac{3}{8}$$
Therefore, time taken by $$\begin{pmatrix}A+B\end{pmatrix}$$ to fill the cistern $$=\dfrac{8}{3}$$ hours $$=2hours\;40\;min$$.
Question 7
1 / -0

In half of a 600 square meters field, a fanner sowed ragi, in one-third of the remaining, he sowed coconut and in one-fourth of the left over, he sowed groundnut. He left half of the remaining land uncultivated. In one-third of the land still left, he dug a well, utilising the remaining land for growing orchids. What fraction of the total land is he using for orchid cultivation?

A
1/36

B
1/28

C
1/16

D
1/12

Solution

$$Lets\quad total\quad land\quad be\quad x,\\ Ragi\quad occupies=\dfrac { 1 }{ 2 } x,\\ Land\quad left=\dfrac { 1 }{ 2 } x,\\ Groundnut\quad occupies=\dfrac { 1 }{ 4 } \times \dfrac { 1 }{ 2 } x=\dfrac { 1 }{ 8 } x,\\ Land\quad left=\dfrac { 3 }{ 8 } x,\\ Coconut\quad occupies=\dfrac { 1 }{ 3 } \times \dfrac { 3 }{ 8 } x=\dfrac { 1 }{ 8 } x,\\ Land\quad left=\dfrac { 1 }{ 4 } x,\\ Land\quad uncultivated=\dfrac { 1 }{ 2 } \times \dfrac { 1 }{ 4 } x=\dfrac { 1 }{ 8 } x=land\quad left,\\ Orchid\quad occupies=\dfrac { 2 }{ 3 } \times \dfrac { 1 }{ 8 } x=\dfrac { 1 }{ 12 } x$$
Question 8
1 / -0

If a pipe fills the tank in $$10$$ minutes, how much minutes it will take to half fill the tank in we connect two pipes?

A
$$20$$

B
$$10$$

C
$$5$$

D
$$2.5$$

Solution

No of pipe (P) is inversely proportional to time (t)
$$\Rightarrow P \propto \dfrac {1}{t}$$
But here it takes $$10$$ minutes to fill the tank.
To half fill the tank the pipe will take $$\dfrac {10}{2} = 5\ minutes$$.
Now, $$P_{1} t_{1} = P_{2} t_{2}$$
$$P_{1} = 1, t_{1} = 5, P_{2} = 2$$, we have to find $$t_{2}$$.
$$\Rightarrow t_{1} = \dfrac {P_{1}t_{1}}{P_{2}} = \dfrac {1\times 5}{2} = 2.5\ minutes$$
Question 9
1 / -0

If $$15$$ men complete a task in $$3$$ days, how many days will $$9$$ men take to complete it?

A
$$3$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

No. of men is inversely proportion to no. of days taken
$$\therefore 15\times 3 = K = 9\times x$$
$$\Rightarrow 4s = 9\times x \Rightarrow x = 5$$.
Question 10
1 / -0

If $$6$$ painters can complete $$9$$ drawing in $$5$$ hours then, what is relation between no. of painters and no. of drawings if no. of hours is constant?

A
Direct

B
Indirect

C
Both

D
None

Solution

$$\because$$ More no. of painters less no. hours taken to complete same no. of drawings
$$\therefore$$ These are in inverse proportion.

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Numerical Applications Test 49

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Numerical Applications Test 49

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SHARING IS CARING

Question 1

$$22$$ days

$$\displaystyle21\frac{1}{2}$$days

$$23$$ days

$$\displaystyle22\frac{1}{2}$$days

Solution

Question 2

$$ 120\ gallons $$

$$ 250 \ gallons $$

$$ 450 \ gallons $$

$$ 500 \ gallons $$

$$ 140 \ gallons $$

Solution

Question 3

$$10$$

$$12$$

$$15$$

$$16$$

Solution

Question 4

$$\dfrac{8}{15}$$

$$\dfrac{2}{15}$$

$$\dfrac{1}{5}$$

$$\dfrac{7}{13}$$

$$\dfrac{16}{15}$$

Solution

Question 5

$$500$$

$$550$$

$$600$$

$$700$$

Solution

Question 6

$$2hrs\;30min$$

$$2hrs\;40min$$

$$2hrs\;50min$$

$$3hrs$$

Solution

Question 7

1/36

1/28

1/16

1/12

Solution

Question 8

$$20$$

$$10$$

$$5$$

$$2.5$$

Solution

Question 9

$$3$$

$$4$$

$$5$$

$$6$$

Solution

Question 10

Direct

Indirect

Both

None

Solution

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