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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Re-Attempt Weekly Quiz Competition

Numerical Applications Test 3

Result

Numerical Applications Test 3

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Rank

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SHARING IS CARING

Question 1

121212

111111

101010

999

Solution

Question 2

505050

42.542.542.5

555555

575757

Solution

Question 3

515151

575757

404040

434343

Solution

Question 4

181818

232323

252525

151515

Solution

Question 5

606060 days

454545 days

545454 days

484848 days

Solution

Question 6

131313

151515

141414

121212

Solution

Question 7

404040 days

353535 days

303030 days

454545 days

Solution

Question 8

55115\displaystyle\frac{5}{11}5115​

56115\displaystyle\frac{6}{11}5116​

65116\displaystyle\frac{5}{11}6115​

66116\displaystyle\frac{6}{11}6116​

Solution

Question 9

0.80.80.8

32.832.832.8

34.834.834.8

33.833.833.8

Solution

Question 10

150150150

149149149

148148148

147147147

Solution

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Question Analysis

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Rank

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$12$

$11$

$10$

$9$

$50$

$42.5$

$55$

$57$

$51$

$57$

$40$

$43$

$18$

$23$

$25$

$15$

$60$ days

$45$ days

$54$ days

$48$ days

$13$

$15$

$14$

$12$

$40$ days

$35$ days

$30$ days

$45$ days

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

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

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

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

$0.8$

$32.8$

$34.8$

$33.8$

$150$

$149$

$148$

$147$