Numerical Applications Test 19

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Numerical Applications Test 19

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Weekly Quiz Competition

Question 1
1 / -0

A alone can do a piece in $$10$$ days and $$B$$ alone can so it in $$15$$ days. In how many days will $$A$$ and $$B$$ together do the same work?

A
$$5$$ days

B
$$6$$ days

C
$$8$$ days

D
$$9$$ days

Solution

We know that,
Number of days $$A$$ required to do piece of work $$=10$$ days
Number of days $$B$$ required to do piece of work $$=15$$ days

$$\therefore$$ We can calculate, work done $$A$$ in $$1$$ day $$=1/10$$
Work done by $$B$$ in $$1$$ days $$=1/15$$

Now, work done by both $$A$$ and $$B$$ together in $$1$$ day $$=1/10+1/15=10/60=1/6$$

$$\therefore A$$ and $$B$$ can do work together in $$6$$ days
Question 2
1 / -0

$$20$$ persons are invited for a party, then the number of ways in which they and the host be seated at a round table is

A
20!

B
21!

C
22!

D
2.20!

Solution

Total no. of persons including host are $$(20+1)$$
As they have to sit in round table, the required permutation is $$(n-1)!$$
$$=(20+1-1)!$$
$$=20!$$
Question 3
1 / -0

The number of ways in which 7 persons can be arranged around a circle is:

A
$$360$$

B
$$720$$

C
$$5040$$

D
$$1440$$

Solution

$$no$$ of ways of arranging n persons in a circle is $$(n-1)!=(7-1)=6!=720$$
Question 4
1 / -0

A factory requires $$42$$ machines to produce a given number of articles in $$63$$ days. How many machines would be required to produce the same number of articles in $$54$$ days?

A
$$49$$ machines

B
$$32$$ machines

C
$$54$$ machines

D
$$31$$ machines

Solution

$$\textbf{Hint: Recall the concept of direct and inverse proportion}$$

$$\textbf{Step 1: Evaluate the given word problem using Inverse proportion}$$
$$\text{Given}$$
$$42$$ $$\text{machines are required to produce article in}$$ $$63$$ $$\text{days}$$
$$\text{ We need to find number of machines required to produce articles in}$$ $$54$$ $$\text{days}$$
$$\text{Let number of machines be x}$$
$$\text{ As we increases the total number of machines time takes to produce the articles decreases. So, they are in}$$
$$\text{inverse proportion.}$$
$$\textbf{Step 2: use}$$ $$(x_1,y_1=x_2,y_2)$$ $$\textbf{form to evaluate}$$
$$42\times 63=x\times 54$$
$$x=\dfrac{42\times 63}{54}$$
$$x=7\times7$$
$$x=49$$
$$\textbf{Option A is correct.}$$
Question 5
1 / -0

The mean of five numbers is $$30$$. If one number is excluded, their mean becomes $$28$$. The excluded number is:

A
$$28$$

B
$$30$$

C
$$35$$

D
$$38$$

Solution

The mean of $$5$$ numbers $$=30$$
The sum of $$5$$ numbers is $$=30\times5 = 150$$

After excluding a number say, $$x$$
Mean $$= 28$$
Sum of four numbers $$= 28\times4 = 112$$

$$x = 150 -112 = 38$$
Question 6
1 / -0

Ten pipes of the same type can fill up a tank in $$16$$ minutes. If two pipes go out of order, how long will the remaining pipes take to fill the tank ?

A
$$18$$ mins

B
$$20$$ mins

C
$$22$$ mins

D
$$24$$ mins

Solution

If $$x$$ is the required number of hour then,
In order to solve this problem, first, we need to find out whether the proportionality is direct or inverse.
Now, here we note that:
For more number of pipes, the time required to fill is less.
For less number of pipes, the time required to fill is more.
Hence, there is an inverse proportionality.
$$10\times 16 = (10-2)\times x$$
where, x is the time required.
$$\Rightarrow 10\times 16 = 8\times x$$
$$\Rightarrow x = \cfrac{10\times 16}{8}$$
$$= 10\times 2$$
$$=20$$ mins.
Question 7
1 / -0

Two persons could fit new windows in a house in $$3$$ days. One of the persons fell ill before the work started. How long days would the job take now?

A
$$3$$

B
$$4$$

C
$$6$$

D
$$9$$

Solution

No. of persons Time taken
$$2$$ $$3$$ days
$$1$$ $$x$$ days
By inverse proportion,
$$2$$ x $$3=1$$ x $$x$$
$$\therefore x= 6$$
Answer is $$6$$ days
Question 8
1 / -0

If $$5$$ workers can build a fence in $$65$$ days, how long would it take $$13$$ workers to build the same fence?

A
$$15$$ days

B
$$20$$ days

C
$$25$$ days

D
$$35$$ days

Solution

More the workers, lesser will be the time it will take to build the fence.
Let $$x$$ be the number of days required to build the fence.
In the equation form, we get
$$5\times 65 = 13\times x$$
$$\therefore x = \cfrac{5\times 65}{13}$$
$$= 5\times 5 = 25$$
Question 9
1 / -0

$$3$$ persons weave $$168$$ shawls in $$14$$ days, how many shawls will 8 people weave in $$5 $$ days?

A
$$90$$

B
$$105$$

C
$$115$$

D
$$160$$

Solution

b'
Set the proportion for number of persons with the number of shawls. Both the quantities are in direct ratio.
Here, we are asked to find out the number of shawls, we compare each item with the number of shawls as shown below :
More number of persons $$\Rightarrow$$ More shawls
Less number of persons $$\Rightarrow$$ Less shawls
i.e. the relationship is direct.
Also, More number of days $$\Rightarrow$$ More shawls
Less number of days $$\Rightarrow$$ Less shawls
i.e. the relationship is direct.
Persons 3 : 8 : : 168 : x
Days 14 : 5

$$\therefore \dfrac{3}{8}\times \dfrac{14}{5} = \dfrac{168}{x}$$

$$\therefore 3\times 14\times x = 168\times 8\times 5$$

$$\Rightarrow x = \dfrac{168\times 8\times 5}{3\times 14} = 160\ shawls $$
'
Question 10
1 / -0

$$15$$ labourers can fill $$35$$ boxes in $$7$$ days. How many labourers can fill $$65$$ boxes in $$5$$ days ?

A
$$13$$

B
$$39$$

C
$$45$$

D
$$55$$

Solution

b'
Number of labourers is directly proportional to the number of boxes and number of boxes is directly proportional to number of days. Set the proportions and solve.
We are asked to find out the number of labourers So we, compare each item with the number of labourers as below.
More number of boxes ⇒'39

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Numerical Applications Test 19

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Numerical Applications Test 19

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SHARING IS CARING

Question 1

$$5$$ days

$$6$$ days

$$8$$ days

$$9$$ days

Solution

Question 2

20!

21!

22!

2.20!

Solution

Question 3

$$360$$

$$720$$

$$5040$$

$$1440$$

Solution

Question 4

$$49$$ machines

$$32$$ machines

$$54$$ machines

$$31$$ machines

Solution

Question 5

$$28$$

$$30$$

$$35$$

$$38$$

Solution

Question 6

$$18$$ mins

$$20$$ mins

$$22$$ mins

$$24$$ mins

Solution

Question 7

$$3$$

$$4$$

$$6$$

$$9$$

Solution

Question 8

$$15$$ days

$$20$$ days

$$25$$ days

$$35$$ days

Solution

Question 9

$$90$$

$$105$$

$$115$$

$$160$$

Solution

Question 10

$$13$$

$$39$$

$$45$$

$$55$$

Solution

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