Numerical Applications Test 3

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Numerical Applications Test 3

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Weekly Quiz Competition

Question 1
1 / -0

Find the mean of:
$$5, 15, 20, 8$$ and $$12$$.

A
$$12$$

B
$$11$$

C
$$10$$

D
$$9$$

Solution

The observations are: $$5, 15, 20, 8, 12$$
Mean $$= \cfrac{\text{Sum}}{\text{Number of observations}}$$
Mean $$= \cfrac{5 + 15 + 20 + 8 + 12}{5}$$
mean $$= \cfrac{60}{5} = 12$$
Question 2
1 / -0

Find the mean of $$43, 51, 50, 57$$ and $$54$$

A
$$50$$

B
$$42.5$$

C
$$55$$

D
$$57$$

Solution

The observations are : $$43, 51, 50, 57$$ and $$54$$
mean $$= \cfrac{\text{Sum}}{\text{Count of numbers}}$$
mean $$= \cfrac{43 + 51 + 50 +57 +54}{5}$$
mean $$= \cfrac{255}{5}$$
mean $$= 51$$
Question 3
1 / -0

Find the mean of $$43, 51, 50, 57$$ and $$54$$.

A
$$51$$

B
$$57$$

C
$$40$$

D
$$43$$

Solution

Mean of $$43, 51, 50, 57, 54$$
Mean $$= \cfrac{\text{Sum}}{\text{Number of observations}}$$
Mean $$= \cfrac{43 + 51 + 50 + 57 + 54}{5} = \cfrac{255}{5} = 51$$
Question 4
1 / -0

Find the mean of the following data: $$18, 33, 30, 21$$ and $$13$$.

A
$$18$$

B
$$23$$

C
$$25$$

D
$$15$$

Solution

Given set of data is $$18,33,30,21,13$$
Arranging the data in ascending order, we get $$13,18,21,30,33$$
No of terms(numbers) $$=n=5$$
Mean $$=\dfrac{\text{Sum of numbers}}{n}$$
$$=\dfrac{13+18+21+30+33}{5}=\dfrac{115}{5}=23$$
Thus, Mean of given data is $$23$$.
Hence, option B is correct.
Question 5
1 / -0

$$12$$ men can complete a piece of work in $$16$$ days. How many days will $$4$$ men take to complete the task?

A
$$60$$ days

B
$$45$$ days

C
$$54$$ days

D
$$48$$ days

Solution

$$1$$ man will complete the job in $$16 \times 12 $$ days.
So, $$4$$ will do in $$\displaystyle \frac{12 \times 16}{4} = 48$$ days.
Question 6
1 / -0

Find the mean of the observations $$8, 12, 16, 22, 10$$ and $$4$$.

A
$$13$$

B
$$15$$

C
$$14$$

D
$$12$$

Solution

The given observations are: $$8, 12, 16, 10, 22, 4$$
Mean $$= \cfrac{\text{Sum}}{\text{Number of observations}}$$
Mean $$= \cfrac{8+ 12 + 16 + 10 + 22 + 4}{6} = \cfrac{72}{6} = 12$$
Question 7
1 / -0

$$A$$ does half as much work as $$B$$ in three fourth of the time. If together they take 18 days to complete a work, how much time shall $$B$$ take to do it?

A
$$40$$ days

B
$$35$$ days

C
$$30$$ days

D
$$45$$ days

Solution

Let $$B$$ complete the work in $$x$$ days.
$$\Rightarrow B$$'s 1 days' work $$= \displaystyle\frac { 1 }{ x }$$

$$\therefore A$$ complete $$\displaystyle\frac { 1 }{ 2 }$$ of the work in $$\displaystyle\frac { 3x }{ 4 }$$ days

$$\Rightarrow A$$'s 1 days' work $$= \displaystyle\frac { \displaystyle\frac { 1 }{ 2 } }{ \displaystyle\frac { 3x }{ 4 } } = \displaystyle\frac { 2 }{ 3x }$$

Given, $$\displaystyle\frac { 1 }{ x } + \displaystyle\frac { 2 }{ 3x } = \displaystyle\frac { 1 }{ 18 }$$

$$\Rightarrow \displaystyle\frac { 3+2 }{ 3x } = \displaystyle\frac { 1 }{ 18 } \Rightarrow \displaystyle\frac { 5 }{ 3x } = \displaystyle\frac { 1 }{ 18 }$$

$$\Rightarrow 3x = 90 \Rightarrow x = 30$$
Question 8
1 / -0

$$P$$ can complete a work in $$12$$ days working $$8$$ hours a day. $$Q$$ can complete the same work in $$8$$ days working $$10$$ hours a day. If both $$P$$ and $$Q$$ work together, working $$8$$ hours a day, in how many days can they complete the work?

A
$$5\displaystyle\frac{5}{11}$$

B
$$5\displaystyle\frac{6}{11}$$

C
$$6\displaystyle\frac{5}{11}$$

D
$$6\displaystyle\frac{6}{11}$$

Solution

$$P$$ can complete the work in $$\left( 12 \times 8 \right)$$ hours $$ = 96$$ hours
$$\therefore   P$$'s 1 hours' work $$= \displaystyle\frac { 1 }{ 96 }$$
$$Q$$ can complete the work in $$\left( 8 \times 10 \right)$$ hours $$ = 80$$ hours
$$\therefore   Q$$'s 1 hours' work $$= \displaystyle\frac { 1 }{ 80 }$$
$$\therefore   \left( P + Q \right)$$'s 1 hours' work $$ = \displaystyle\frac { 1 }{ 96 } + \displaystyle\frac { 1 }{ 80 } = \displaystyle\frac { 5+6 }{ 480 } = \displaystyle\frac { 11 }{ 480 }$$
$$\therefore   \left( P+Q \right)$$ can complete the whole work in $$ \displaystyle\frac { 480 }{ 11 }$$ hours.
$$\therefore$$ Working 8 hours a day, $$P$$ and $$Q$$ can complete the whole work in $$\left( \displaystyle\frac { 480 }{ 11 } \times \displaystyle\frac { 1 }{ 8 } \right)$$ days $$ = \displaystyle\frac { 60 }{ 11 }$$ days $$ = 5 \displaystyle\frac { 5 }{ 11 } $$ days.
Question 9
1 / -0

The average of eight numbers is $$38.4$$ and the average of seven of them is $$39.2$$. What is the eighth number?

A
$$0.8$$

B
$$32.8$$

C
$$34.8$$

D
$$33.8$$

Solution

Sum of eight numbers $$= 38.4 \times 8 = 307.2$$
$$\because $$ Total sum $$=$$ Average $$\times$$ Number of items
Sum of seven numbers $$=39.2 \times 7 = 274.4$$
$$\therefore$$ Eight number $$= 307.2 - 274.4 = 32.8$$
Question 10
1 / -0

The runs scored by Sachin in $$5$$ test matches are $$140$$, $$153$$, $$148$$, $$150$$ and $$154$$ respectively. Find his mean

A
$$150$$

B
$$149$$

C
$$148$$

D
$$147$$

Solution

Runs score by Sachin in $$5$$ test matches: $$140,153,148,150,154$$
Mean of runs $$= \cfrac{\text{Total runs}}{\text{Number of matches}}$$
Mean $$= \cfrac{140 + 153 + 148 + 150 + 154}{5}$$
Mean $$= \cfrac{745}{5}$$
Mean $$= 149$$

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Numerical Applications Test 3

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Numerical Applications Test 3

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SHARING IS CARING

Question 1

$$12$$

$$11$$

$$10$$

$$9$$

Solution

Question 2

$$50$$

$$42.5$$

$$55$$

$$57$$

Solution

Question 3

$$51$$

$$57$$

$$40$$

$$43$$

Solution

Question 4

$$18$$

$$23$$

$$25$$

$$15$$

Solution

Question 5

$$60$$ days

$$45$$ days

$$54$$ days

$$48$$ days

Solution

Question 6

$$13$$

$$15$$

$$14$$

$$12$$

Solution

Question 7

$$40$$ days

$$35$$ days

$$30$$ days

$$45$$ days

Solution

Question 8

$$5\displaystyle\frac{5}{11}$$

$$5\displaystyle\frac{6}{11}$$

$$6\displaystyle\frac{5}{11}$$

$$6\displaystyle\frac{6}{11}$$

Solution

Question 9

$$0.8$$

$$32.8$$

$$34.8$$

$$33.8$$

Solution

Question 10

$$150$$

$$149$$

$$148$$

$$147$$

Solution

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