Numerical Applications Test 40

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Numerical Applications Test 40

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Weekly Quiz Competition

Question 1
1 / -0

Ram can do a price of work in $$6$$ days and Shyam can finish the same work in $$12$$ days. How much work will be finished if both work together for $$2$$ days?

A
One-fourth of the work

B
One-third of the work

C
Half of the work

D
Whole of the work

Solution

Since, Ram can do a piece of work in $$6$$ days

Therefore, One day's work of Ram $$= \dfrac {1}{6}$$

Shyam can finish the same work in $$12$$ days

Therefore One day's work of Shyam $$= \dfrac {1}{12}$$

Hence, one day's work of them, if they work together

$$\dfrac { 1 }{ 6 } +\dfrac { 1 }{ 12 } =\dfrac { 2 }{ 12 } +\dfrac { 1 }{ 12 } =\dfrac { 3 }{ 12 } =\dfrac { 1 }{ 4 } $$

Therefore, two days' work of them is:

$$\dfrac { 1 }{ 4 } \times 2=\dfrac { 1 }{ 2 } $$

Hence, if they work together for $$2$$ days, then half of the work will be finished.
Question 2
1 / -0

A can do a piece of work in $$6\dfrac {2}{3}$$ days and B in $$5$$ days. They work together for $$2$$ days and then A leaves B to finish the work alone. How long will B take to finish it?

A
$$\dfrac {3}{4}$$ days

B
$$1\dfrac {1}{2}days$$

C
$$3\ days$$

D
$$7\ days$$

Solution
Question 3
1 / -0

$$1200$$ men in a fort have provisions for $$28$$ days. After $$4$$ days, $$300$$ men leave the fort. How long will food last now?

A
$$28$$

B
$$32$$

C
$$30$$

D
$$18$$

Solution

Given that fort had provision of food for $$1200$$ men for $$28$$ days.

Therefore, after $$4$$ days, the remaining food is sufficient for $$1200$$ men for $$24$$ days

Remaining men after $$4$$ days $$= 1200 - 300 = 900$$

Assume that after $$4$$ days,the remaining food is sufficient for $$900$$ men for $$x$$ days

Now, we find for how long food lasts for $$900$$ men is as follows:

$$\dfrac { 1200 }{ 900 } =\dfrac { x }{ 24 } \\ \Rightarrow x=\dfrac { 1200 }{ 900 } \times 24\\ \Rightarrow x=\dfrac { 4 }{ 3 } \times 24\\ \Rightarrow x=4\times 8\\ \Rightarrow x=32$$

Hence, the food lasts for $$32$$ days now.
Question 4
1 / -0

In how many ways $$7$$ men and $$7$$ women can be seated around a round table such that no two women can sit together?

A
$$(7!)^2$$

B
$$7!\times 6!$$

C
$$(6!)^2$$

D
$$7!$$

Solution

Lets first place the men (M). * here indicates the linker of round table *M -M - M - M - M* which is in $$(7-1)!$$ ways = $$6!$$
So we have to place the women in between the men which is on the $$5$$ empty seats So $$7$$ women can sit on $$7$$ seats in $$(7)!$$ ways
So the answer is $$7!\times 6!$$
Question 5
1 / -0

A can copy $$75$$ pages in $$25$$ hours, A and B together copy $$135$$ pages in $$27$$ hours. In what time can B copy $$42$$ pages?

A
$$17\ hours$$

B
$$27\ hours$$

C
$$31\ hours$$

D
$$21\ hours$$

Solution
Question 6
1 / -0

Two pipes $$A$$ and $$B$$ can fill a cistern in $$37\displaystyle\frac{1}{2}$$ minutes and $$45\ minutes $$ respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the $$B$$ is turned off after :

A
$$5\ min$$

B
$$9\ min$$

C
$$10\ min$$

D
$$15\ min$$

Solution

Let B be turned off after x minutes. Then,
Part filled by $$(A+B)$$ in x min. $$+$$ Part filled by A in $$(30-x)$$min. $$=1$$.
$$\therefore x\left(\displaystyle\frac{2}{75}+\dfrac{1}{45}\right)+(30-x).\displaystyle\dfrac{2}{75}=1$$
$$\Rightarrow \displaystyle\dfrac{11x}{225}+\dfrac{(60-2x)}{75}=1$$
$$\Rightarrow 11x+180-6x=225$$.
$$\Rightarrow x=9$$.
Question 7
1 / -0

A pump can fill a tank with water in $$2\ hours$$. Because of a leak, it took $$2\displaystyle\frac{1}{3}\ hours$$ to fill the tank. The leak can drain all the water of the tank in.

A
$$\displaystyle 4\frac{1}{3}\ hrs$$

B
$$\displaystyle 7\ hrs$$

C
$$\displaystyle 8\ hrs$$

D
$$\displaystyle 14\ hrs$$

Solution

Rate of filling the Tank by Pump : $$\dfrac{1}{2} $$
Rate of leak while water is being pumped in the tank: $$\dfrac{3}{7}$$

Rate of leak in the tank: $$1$$ hour $$=\left(\displaystyle\frac{1}{2}-\frac{3}{7}\right)=\displaystyle\frac{1}{14}$$.
$$\therefore$$ Leak will empty the tank in $$14$$ hrs.
Question 8
1 / -0

Which of the following is correct?

A
When the positions are numbered, then the circular permutations are treated as a linear arrangement.

B
In linear arrangements, it does not make difference whether the positions are numbered are not.

C
Both A and B

D
None of these.

Solution

By numbering position we are actually fixing staring point which makes it similar to linear permutation.so option A is correct
Linear permutation already has a staring point so it dose not need seats to be numbered so option B is correct
Question 9
1 / -0

Two pipes P and Q would fill a cistern in $$24$$ and $$32$$ minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in $$16$$ minutes

A
After $$12\ min.$$

B
After $$6\ min.$$

C
After $$15\ min.$$

D
After $$20\ min.$$

Solution
Question 10
1 / -0

A cistern has a leak which would empty it in $$8$$ hours. A tap is turned on which admits $$6$$ litres a minute into the cistern and is now emptied in $$12$$ hours. How many litres does the cistern hold?

A
$$8640$$

B
$$8500$$

C
$$4320$$

D
$$60\ hours$$

Solution

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Re-Attempt Weekly Quiz Competition

Numerical Applications Test 40

Result

Numerical Applications Test 40

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Rank

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SHARING IS CARING

Question 1

One-fourth of the work

One-third of the work

Half of the work

Whole of the work

Solution

Question 2

$$\dfrac {3}{4}$$ days

$$1\dfrac {1}{2}days$$

$$3\ days$$

$$7\ days$$

Solution

Question 3

$$28$$

$$32$$

$$30$$

$$18$$

Solution

Question 4

$$(7!)^2$$

$$7!\times 6!$$

$$(6!)^2$$

$$7!$$

Solution

Question 5

$$17\ hours$$

$$27\ hours$$

$$31\ hours$$

$$21\ hours$$

Solution

Question 6

$$5\ min$$

$$9\ min$$

$$10\ min$$

$$15\ min$$

Solution

Question 7

$$\displaystyle 4\frac{1}{3}\ hrs$$

$$\displaystyle 7\ hrs$$

$$\displaystyle 8\ hrs$$

$$\displaystyle 14\ hrs$$

Solution

Question 8

When the positions are numbered, then the circular permutations are treated as a linear arrangement.

In linear arrangements, it does not make difference whether the positions are numbered are not.

Both A and B

None of these.

Solution

Question 9

After $$12\ min.$$

After $$6\ min.$$

After $$15\ min.$$

After $$20\ min.$$

Solution

Question 10

$$8640$$

$$8500$$

$$4320$$

$$60\ hours$$

Solution

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