Numerical Applications Test 35

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Numerical Applications Test 35

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Weekly Quiz Competition

Question 1
1 / -0

If $$10$$ workers can do a work in $$15$$ hours then $$30$$ workers can do it in _____ hours

A
$$5$$

B
$$10$$

C
$$15$$

D
$$30$$

Solution

This question is based on Inverse proprtion
According to the given conditions,
No. of workers Time taken
$$10$$ $$15$$ hours
$$30$$ $$x$$ days
By inversion proportion,
$$10\times15 = 30\times x$$
$$\therefore x = \dfrac{10\times15}{30}$$
$$\therefore x =5$$
Answer is $$5$$ hours
Question 2
1 / -0

Two pipes A and B can fill a tank in $$20$$ and $$30$$ minutes respectively. If both the pipes are used together, then how long it will take to fill the tank?

A
$$11$$ mins

B
$$12$$ mins

C
$$13$$ mins

D
$$15$$ mins

Solution

Part filled by A in $$1$$ min $$=\dfrac{1}{20}$$
Part filled by B in $$1$$ min $$=\dfrac{1}{30}$$
Part filled by $$\begin{pmatrix}A+B\end{pmatrix}$$ in $$1$$ min $$=\dfrac{1}{20}+\dfrac{1}{30}=\dfrac{1}{12}$$
So both pipes can fill the tank in $$12$$ mins.
Question 3
1 / -0

A tap A can fill a cistern in $$4$$ hours and the tap B can empty the full cistern in $$6$$ hours. If both the taps are opened together in the empty cistern, in how much time will the cistern be filled up?

A
$$8hrs$$

B
$$10hrs$$

C
$$12hrs$$

D
$$14hrs$$

Solution

Time taken by tap A to fill the cistern $$=4\;hours$$.
Work done by tap A in $$1$$ hour $$=\dfrac{1}{4}$$
Time taken by tap B to empty the full cistern $$=6\;hours$$.
Work done by tap B in $$1$$ hour $$=-\dfrac{1}{6}$$ (since, tap B empties the cistern).
Work done by $$\begin{pmatrix}A+B\end{pmatrix}$$ in $$1$$ hour $$\dfrac{1}{4}-\dfrac{1}{16}=\dfrac{3-2}{12}=\dfrac{1}{12}$$ part of the tank is filled.
Therefore, the tank will fill the cistern $$=12\;hours$$.
Question 4
1 / -0

A and B together can complete a work in $$4$$ days. A alone can finish the work in $$12$$ days, In how many days B alone can finish the work?

A
$$5$$

B
$$15$$

C
$$6$$

D
$$8$$

Solution

$$\begin{pmatrix}A+B\end{pmatrix}$$"s $$1$$ day work $$=\dfrac{1}{4}$$
A"s $$1$$ day work $$=\dfrac{1}{12}$$
B"s $$1$$ day work $$=\begin{bmatrix}\begin{pmatrix}\dfrac{1}{4}\end{pmatrix}-\begin{pmatrix}\dfrac{1}{12}\end{pmatrix}\end{bmatrix}=\dfrac{1}{6}$$
So, B can complete the work in $$6$$ days
Question 5
1 / -0

A group of workers can do a piece of work in $$24$$ days. However as $$7$$ of them were absent it took $$30$$ days to complete work. How many people actually worked on the job to complete it?

A
$$28$$

B
$$35$$

C
$$30$$

D
$$42$$

Solution

Let the original number of workers in the group be "$$ x$$"
therefore, actual number of workers $$=x-7$$.
We know that the number of man hours required to do the job is the same in both the cases.
Therefore, $$x\begin{pmatrix}24\end{pmatrix}=\begin{pmatrix}x-7\end{pmatrix}.30$$
$$\Longrightarrow 24x=30x-210$$
$$\Longrightarrow 6x=210$$
$$\Longrightarrow x=35$$.
Therefore, the actual number of workers who worked to complete the job $$=x-7=35-7=28$$.
Question 6
1 / -0

Pipe A can fill a tank in $$5$$ hours, pipe B in $$10$$ hours and pipe C in $$30$$ hours. If all the pipes are open, in how many hours will the tank be filled?

A
$$3$$ hrs

B
$$2$$ hrs

C
$$2.5$$ hrs

D
$$3.5$$ hrs

Solution

Part filled by A in $$1$$ hour $$=\dfrac{1}{5}$$
Part filled by B in $$1$$ hour $$=\dfrac{1}{10}$$
Part filled by C in $$1$$ hour $$=\dfrac{1}{30}$$
Part filled by $$\begin{pmatrix}A+B+C\end{pmatrix}$$ in $$1$$ hour $$=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{30}=\dfrac{1}{3}$$
Question 7
1 / -0

If $$16$$ workers can do a work in $$20$$ hours then how many workers can do the work in $$10$$ hours?

A
$$8$$

B
$$16$$

C
$$32$$

D
$$24$$

Solution

This question is based on Inverse proprtion
According to the given conditions,
No. of workers Time taken
$$16$$ $$20$$ hours
$$x$$ $$10$$ hours
By inversion proportion,
$$16\times20 = x\times10$$
$$\therefore x = \dfrac{16\times20}{10}$$
$$\therefore x =32$$
Answer is $$32$$ workers
Question 8
1 / -0

$$3$$ pipes are required to fill a tank in $$1$$ hour. How long it will take to fill a tank by $$5$$ pipes?

A
$$8$$

B
$$12$$

C
$$24$$

D
$$36$$

Solution

This question is based on Inverse proprtion
According to the given conditions,
No. of pipes Time taken
$$3$$ $$1$$ hours
$$5$$ $$x$$ hours
By inversion proportion,
$$3\times1 = 5\times x$$
$$\therefore x = \dfrac{3\times1}{5}$$
$$\therefore x = 0.6$$ hours
$$\therefore x = 0.6$$ hours$$\times60$$ minutes $$ = 36$$ minutes
Answer is $$36$$ minutes
Question 9
1 / -0

$$15$$ persons complete a work in $$4$$ days by working $$6$$ hours a day. How many days it will take to complete the work if $$5$$ persons work same hours per day?

A
$$20$$

B
$$30$$

C
$$12$$

D
$$18$$

Solution

No of person is inversely proportional to the no of days.
Again, no of hours is inversely proportional to the no of days.
So, $$15\times 4 = k = 5\times x$$
$$\Rightarrow x = 12$$; taking no of hours per day constant.
Question 10
1 / -0

What is the proportionality between the production of cakes & days and production of cakes & hours respectively?

A
direct, direct respectively

B
direct, inverse respectively

C
inverse, direct respectively

D
none of these

Solution

If no of days increase, no of cakes increase accordingly. Similarly, if no of hours increase, no of cakes increase accordingly.
Hence, both are in direct proportions.

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Numerical Applications Test 35

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Numerical Applications Test 35

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Question 1

$$5$$

$$10$$

$$15$$

$$30$$

Solution

Question 2

$$11$$ mins

$$12$$ mins

$$13$$ mins

$$15$$ mins

Solution

Question 3

$$8hrs$$

$$10hrs$$

$$12hrs$$

$$14hrs$$

Solution

Question 4

$$5$$

$$15$$

$$6$$

$$8$$

Solution

Question 5

$$28$$

$$35$$

$$30$$

$$42$$

Solution

Question 6

$$3$$ hrs

$$2$$ hrs

$$2.5$$ hrs

$$3.5$$ hrs

Solution

Question 7

$$8$$

$$16$$

$$32$$

$$24$$

Solution

Question 8

$$8$$

$$12$$

$$24$$

$$36$$

Solution

Question 9

$$20$$

$$30$$

$$12$$

$$18$$

Solution

Question 10

direct, direct respectively

direct, inverse respectively

inverse, direct respectively

none of these

Solution

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