Numerical Applications Test 11

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Numerical Applications Test 11

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Question 1
1 / -0

In how many days can $$10$$ women finish a work?
$$I$$. $$10$$ men can complete the work in $$6$$ days.
$$II$$. $$10$$ men and $$10$$ women together can complete the work in $$3\cfrac{3}{7}$$ days.
$$III$$. If $$10$$ men work for $$3$$ days and thereafter $$10$$ women replace them, the remaining work in completed in $$4$$ days.

A
Any two of the three

B
$$I$$ and $$II$$ only

C
$$II$$ and $$III$$ only

D
$$I$$ and $$III$$ only

E
None of these

Solution

$$I$$. $$(10\times 6)$$ men can complete the work in $$1$$ day.
$$\Rightarrow$$ $$1$$ man's $$1$$ day's work $$=\cfrac{1}{60}$$
$$II$$. $$(10\times \cfrac{24}{7})men+(10\times \cfrac{24}{7})women$$ can complete the work in $$1$$ day.
$$\Rightarrow$$ $$\left( \cfrac { 240 }{ 7 } \right) $$ men's $$1$$ day work $$+\left( \cfrac { 240 }{ 7 } \right) $$ women's $$1$$ day work $$=1$$
$$\Rightarrow$$ $$\left( \cfrac { 240 }{ 7 } \times \cfrac { 1 }{ 60 } \right) +\left( \cfrac { 240 }{ 7 } \right) $$ women's $$1$$ day Work $$=1$$.
$$\Rightarrow$$ $$\left( \cfrac { 240 }{ 7 } \right) $$ women's $$1$$ day work $$=\left( 1-\cfrac { 4 }{ 7 } \right) =\cfrac { 3 }{ 7 } $$
$$\Rightarrow$$ $$10$$ women's $$1$$ day's work $$=\left( \cfrac { 3 }{ 7 } \times \cfrac { 240 }{ 7 } \times 10 \right) =\cfrac{1}{8}$$
So, $$10$$ women can finish the work in $$8$$ days.
$$III$$. ($$10$$ men'w work for $$3$$ days)$$+$$ ($$10$$ women's work for $$4$$ days)$$=1$$
$$\Rightarrow$$ $$(10\times 3)$$ men's $$1$$ day's work $$+$$ $$(10\times 4)$$ women's $$1$$ day's work $$=1$$
$$\Rightarrow$$ $$30$$ men's $$1$$ day's work $$+$$ $$40$$ women's $$1$$ day's work $$=1$$
Thus, $$I$$ and $$III$$ will give us the answer.
And, $$II$$ and $$III$$ will give us the answer.
$$\therefore$$ Correct answer is (A).
Question 2
1 / -0

$$A$$ and $$B$$ can do a job together in $$7$$ days. $$A$$ is $$1\cfrac{3}{4}$$ times as efficient as $$B$$. The same job can be done by $$A$$ alone in:

A
$$9\cfrac{1}{3}$$ days

B
$$11$$ days

C
$$12\cfrac{1}{4}$$ days

D
$$16\cfrac{1}{3}$$ days

Solution

($$A$$'s $$1$$ day's work):($$B$$'s $$1$$ day's work)$$=\cfrac{7}{4}=7:4$$.
Let $$A$$'s and $$B$$'s $$1$$ day's work be $$7x$$ and $$4x$$ respectively.
Then, $$7x+4x=\cfrac{1}{7}$$ $$\Rightarrow$$ $$11x=\cfrac{1}{7}$$ $$\Rightarrow$$ $$x=\cfrac{1}{77}$$
$$\therefore$$ $$A$$'s $$1$$ day's work $$=\left( \cfrac { 1 }{ 77 } \times 7 \right) =\cfrac { 1 }{ 11 } $$.
Question 3
1 / -0

How many worker are required for completing the construction work in $$10$$ days?
$$I$$. $$20$$% of the work can be completed by $$8$$ workers in $$8$$ days.
$$II$$. $$20$$ workers can complete the work in $$16$$ days.
$$III$$. One-eighth of the work can be completed by $$8$$ workers in $$5$$ days.

A
$$I$$ only

B
$$II$$ and $$III$$ only

C
$$III$$ only

D
$$I$$ and $$III$$ only

E
Any one of the three

Solution

$$I$$. $$\cfrac{20}{100}$$ work can be completed by $$(8\times 8)$$ workers in $$1$$ day.
$$\Rightarrow$$ Whole work can be completed by $$(8\times 8\times 5)$$ workers in $$1$$ day.
$$=\cfrac{8\times 8\times 5}{10}$$ workers in $$10$$ days $$=32$$ workers in $$10$$ days.
$$II$$. $$(20\times 16)$$ workers can finish it in $$1$$ day.
$$\Rightarrow$$ $$\cfrac{(20\times 16)}{10}$$ workers can finish it in $$10$$ days.
$$\Rightarrow$$ $$32$$ workers can finish it in $$10$$ days.
$$III$$. $$\cfrac{1}{8}$$ work can be completed by $$(8\times 5)$$ workers in $$1$$ day.
$$\Rightarrow$$ Whole work can be completed by $$(8\times 5\times 8)$$ workers in $$1$$ day.
$$=\cfrac{8\times 5\times 8}{10}$$ workers in $$10$$ days $$=32$$ workers in $$10$$ days.
$$\therefore$$ Any one of the three gives the answer.
$$\therefore$$ Correct answer is (E).
Question 4
1 / -0

$$8$$ men and $$14$$ women are working together in a field. After working for $$3$$ days, $$5$$ men and $$8$$ women leave the work. How many more days will be required to complete the work?
$$I$$. $$19$$ men and $$12$$ women together can complete the work in $$18$$ days.
$$II$$. $$16$$ men can complete two-third of the work in $$16$$ days.
$$III$$. In $$1$$ day, the work done by three men in equal to the work done by four women.

A
$$I$$ only

B
$$II$$ only

C
$$III$$ only

D
$$I$$ or $$II$$ or $$III$$

E
$$II$$ or $$III$$ only

Solution

Clearly, $$I$$ only gives the answer.
Similarly, $$II$$ only gives the answer.
And, $$III$$ only gives the answer.
$$\therefore$$ Correct answer is (D).
Question 5
1 / -0

How long will Machine $$Y$$, working alone, take to produce $$x$$ candles?
$$I$$. Machine $$X$$ produce $$x$$ candles in $$5$$ minutes.
$$II$$. Machine $$X$$ and Machine $$Y$$ working at the same time produce $$x$$ candles in $$2$$ minutes.

A
$$I$$ alone sufficient while $$II$$ alone not sufficient to answer

B
$$II$$ alone sufficient while $$I$$ alone not sufficient to answer

C
Either $$I$$ or $$II$$ alone sufficient to answer

D
Both $$I$$ and $$II$$ are not sufficient to answer

E
Both $$I$$ and $$II$$ are necessary to answer

Solution

$$I$$. gives, Machine $$X$$ produces $$\cfrac{x}{5}$$ candles in $$1$$ min.
$$II$$. gives, Machine $$X$$ and $$Y$$ produce $$\cfrac{x}{2}$$ candles in $$1$$ min.
From $$I$$ and $$II$$, $$Y$$ produces $$\left( \cfrac { x }{ 2 } -\cfrac { x }{ 5 } \right) =\cfrac { 3x }{ 10 } $$ candles in $$1$$ min.
$$\cfrac{3x}{10}$$ candles are produced by $$Y$$ in $$1$$ min.
$$x$$ candles will be produced by $$Y$$ in $$(\cfrac{10}{3x}xx) min=\cfrac{10}{3}$$ min.
Thus, $$I$$ and $$II$$ both are necessary to get the answer.
$$\therefore$$ Correct answer is (E).
Question 6
1 / -0

$$A$$ and $$B$$ together can complete a task in $$7$$ days. $$B$$ alone can do it in $$20$$ days. What part of the work was carried out by $$A$$?
$$I$$. $$A$$ completed the job alone after $$A$$ and $$B$$ worked together for $$5$$ days.
$$II$$. Part of the work done by $$A$$ could have been done by $$B$$ and $$C$$ together in $$6$$ days.

A
$$I$$ alone sufficient while $$II$$ alone not sufficient to answer

B
$$II$$ alone sufficient while $$I$$ alone not sufficient to answer

C
Either $$I$$ or $$II$$ alone sufficient to answer

D
Both $$I$$ and $$II$$ are not sufficient to answer

E
Both $$I$$ and $$II$$ are necessary to answer

Solution

$$B$$'s $$1$$ day's work $$=\cfrac{1}{20}$$
$$(A+B)$$'s $$1$$ day's work $$=\cfrac{1}{7}$$
$$I$$. $$(A+B)$$'s $$5$$ day's work $$=\cfrac{5}{7}$$
Remaining work $$=\left( 1-\cfrac { 5 }{ 7 } \right) =\cfrac { 2 }{ 7 } $$
$$\therefore$$ $$\cfrac{2}{7}$$ work was carried by $$A$$.
$$II$$. is irrelevant.
$$\therefore$$ Correct answer is (A).
Question 7
1 / -0

Two pipes can fill a tank in $$20$$ and $$24$$ 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
$$60$$ gallons

B
$$100$$ gallons

C
$$120$$ gallons

D
$$180$$ gallons

Solution

Work done by the waste pipe in 1 gallons.
Question 8
1 / -0

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank $$5$$ hours faster than the first pipe and $$4$$ hours slower than the third pipe. The time required by the first pipe is.

A
$$6$$ hours

B
$$10$$ hours

C
$$15$$ hours

D
$$30$$ hours

Solution

Suppose, first pipe alone takes x hours to fill the tank.
Then, second and third pipes will take $$(x-5)$$ and $$(x-9)$$ hours respectively to fill the tank.
$$\therefore \displaystyle\frac{1}{x}+\frac{1}{(x-5)}=\frac{1}{(x-9)}$$
$$\Rightarrow \displaystyle\frac{x-5+x}{x(x-5)}=\frac{1}{(x-9)}$$
$$\Rightarrow (2x-5)(x-9)=x(x-5)$$
$$\Rightarrow x^2-18x+45=0$$
$$(x-15)(x-3)=0$$
$$\Rightarrow x=15$$. [neglecting $$x=3$$]
Question 9
1 / -0

Pipes A and B can fill a tank in $$5$$ and $$6$$ hours respectively. Pipe C can empty it in $$12$$ hours. If all the three pipes are opened together, then the tank will be filled in.

A
$$1\displaystyle\frac{13}{17}$$ hours

B
$$2\displaystyle\frac{8}{11}$$ hours

C
$$3\displaystyle\frac{9}{17}$$ hours

D
$$4\displaystyle\frac{1}{2}$$ hours

Solution

Net part fillef in $$1$$ hour $$\left(\displaystyle\frac{1}{5}+\frac{1}{6}-\frac{1}{12}\right)=\displaystyle\frac{17}{60}$$
$$\therefore$$ The tank will be full in $$\displaystyle\frac{60}{17}$$ hours i.e., $$3\displaystyle\frac{9}{17}$$ hours.
Question 10
1 / -0

A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A
3.6

B
7.2

C
8.4

D
10

Solution

Speed= $$\left ( \frac{600}{5 \times 60} \right )$$ m/sec.
= 2 m/seec.
Converting m/sec to km/hr (see important formula section)
$$\left ( 2\times \frac{18}{5} \right )$$ km/hr
=7.2 km/hr.

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Numerical Applications Test 11

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Question 1

Any two of the three

$$I$$ and $$II$$ only

$$II$$ and $$III$$ only

$$I$$ and $$III$$ only

None of these

Solution

Question 2

$$9\cfrac{1}{3}$$ days

$$11$$ days

$$12\cfrac{1}{4}$$ days

$$16\cfrac{1}{3}$$ days

Solution

Question 3

$$I$$ only

$$II$$ and $$III$$ only

$$III$$ only

$$I$$ and $$III$$ only

Any one of the three

Solution

Question 4

$$I$$ only

$$II$$ only

$$III$$ only

$$I$$ or $$II$$ or $$III$$

$$II$$ or $$III$$ only

Solution

Question 5

$$I$$ alone sufficient while $$II$$ alone not sufficient to answer

$$II$$ alone sufficient while $$I$$ alone not sufficient to answer

Either $$I$$ or $$II$$ alone sufficient to answer

Both $$I$$ and $$II$$ are not sufficient to answer

Both $$I$$ and $$II$$ are necessary to answer

Solution

Question 6

$$I$$ alone sufficient while $$II$$ alone not sufficient to answer

$$II$$ alone sufficient while $$I$$ alone not sufficient to answer

Either $$I$$ or $$II$$ alone sufficient to answer

Both $$I$$ and $$II$$ are not sufficient to answer

Both $$I$$ and $$II$$ are necessary to answer

Solution

Question 7

$$60$$ gallons

$$100$$ gallons

$$120$$ gallons

$$180$$ gallons

Solution

Question 8

$$6$$ hours

$$10$$ hours

$$15$$ hours

$$30$$ hours

Solution

Question 9

$$1\displaystyle\frac{13}{17}$$ hours

$$2\displaystyle\frac{8}{11}$$ hours

$$3\displaystyle\frac{9}{17}$$ hours

$$4\displaystyle\frac{1}{2}$$ hours

Solution

Question 10

3.6

7.2

8.4

10

Solution

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