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13. The average weight of the students of a class is 40 kgs. 5 new students with the average weight of 46 kgs having joined the class, the average weight of the class is increased by 2 kg. Find the number of students in the class originally?
a. 10
b. 12
c. 14
d. 16

Answer: A

Explanation:
Let the number of students = $n$
Sum of the weights of the class originally = $40 \times n$ $=40n$
Sum of the weights of the class after students joined the class = $40n + 5 \times 46 $ $=40n+230$
New average = $\dfrac{{40n + 230}}{{n + 5}} = 42$
$ \Rightarrow 40n + 230 = 42n + 210$
$ \Rightarrow 2n = 10$
$ \Rightarrow n = 5$

14. Average temperature from ${9^{th}}$ to ${16^{th}}$ of a month is ${\rm{30}}^{\rm{o}} {\rm{C}}$ and that from ${10^{th}}$ to ${17^{th}}$ is ${\rm{31}}^{\rm{o}} {\rm{C}}$. What is the temperature on ${17^{th}}$, if temperature on ${9^{th}}$ is ${\rm{35}}^{\rm{o}} {\rm{C}}$?
a. 35
b. 37
c. 39
d. 43

Answer: D

Explanation:
Total days in each case are 8 days.
$9^{th}+10^{th}+...+16^{th}\qquad\quad= 30 \times 8$ $(1)$
$\;\qquad 10^{th}+...+16^{th}+17^{th}$ $= 31 \times 8$ $(2)$
$(2) - (1)$: ${17^{th}} - {9^{th}}$ $= 8 × \left( {{{31}^o}C - {{30}^o}C} \right) = {8^o}C$
Temparature on ${17^{th}}$ = ${35^o}C + {8^o}C = {43^o}C$

15. The average of 11 observations is 72. If average of first 6 observations is 70 and that of last 6 observations is 71, then the 6th observation is:
a. 51
b. 54
c. 55
d. 56

Answer: B

Explanation:
${6^{th}}$ observation = Sum of the first 6 observations + Sum of the last 6 observations - Sum of the 11 observations
${6^{th}}$ observation $ = 70 \times 6 + 71 \times 6 - 72 \times 11$ $=54$

16. Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
a. 350
b. 370
c. 390
d. 430

Answer: C

Explanation:
We have to calculate weighted mean.
$A = \dfrac{{mx + ny}}{{m + n}}$ = $ = \dfrac{{3 \times 350 + 4 \times 420}}{{3 + 4}}$ $ = \text{Rs}.390$
Assumed mean = Rs. 350

17. 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find the amount paid by him.
a. 110
b. 111
c. 115
d. 123

Answer: C

Explanation:
Let the average amount paid by each of 11 friends = $x$
$ \Rightarrow 11x = 10 \times 60 + \left( {x + 50} \right)$
$ \Rightarrow 11x = 600 + x + 50$
$ \Rightarrow 10x = 650$
$ \Rightarrow x = 65$
The amount paid by the 11th person $= x + 50 = 65 + 50 = 115$

18. The average marks obtained by some students in an examination is 54. If 20% of the students got a mean score of 90 marks and the 30% of the students got a mean score of 20. Find the average marks of the remaining students.
a. 60
b. 62
c. 64
d. 66

Answer: A

Explanation:
Remaining students $= 100\% - 20\% - 30\% = 50%$
Let remaining students got a mean score of $x$ marks.
Then, $20\%(90) + 30\% (20) + 50\% (x) = 54$
$ \Rightarrow $ $18 + 6 + 50\% (x) = 54$
$ \Rightarrow $ $50%(x) = 54 - 18 - 6 = 30$
$ \Rightarrow $ $x = 30 × 2 = 60$

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