a, b, c, d, e, f, g are consecutive even numbers. j, k, l, m, n are consecutive odd numbers. The average of all the numbers is :
A. $3\left(\large\frac{a+n}{2}\right)$
B. $\left(\Large\frac{1+d}{2}\right)$
C. $\left(\Large\frac{a+b+m+n}{4}\right)$
D. $3\left(\Large\frac{j+c+n+g}{4}\right)$
Show Answer
Answer-B
Solution-
Solution(By Apex Team)
$\begin{array}{l}\text{According to the question,}\\
\text{Consecutive even numbers}\\
\text{= a, b, c, d, e, f, g}\\
\text{Consecutive odd numbers}\\
\text{= j, k, l, m, n}\\
\text{Consecutive even numbers}\\
\text{2, 4, 6, 8, 10, 12, 14}\end{array}$
$\begin{array}{l}\Large\frac{2+4+6+8+10+12+14}{7}\\
=\Large\frac{56}{7}\\
=8\text{ middle term}\\
\text{Consecutive odd numbers}\\
1,3,5,7,9\\
\Large\frac{1+3+5+7+9}{2}\\
=\Large\frac{25}{5}\\
=5\text{ middle term }\end{array}$
∴ Same as in above situation.
Average of even numbers = d
Average of odd numbers = 1
∴ Average of all numbers
$=\left(\Large\frac{1+d}{2}\right)$
- A grocer has a sale of Rs. 6435, Rs. 6927…
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A. Rs. 4991 B. Rs. 5991 C. Rs. 6001 D. Rs. 6991 Answer: Option AShow Answer
Solution(By Apex Team)
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) $\begin{array}{l}\text{= Rs. 34009}\\ \text{∴ Required sale}\\ \text{= Rs. [(6500 × 6) – 34009]}\\ \text{= Rs. (39000 – 34009)}\\ \text{= Rs. 4991}\end{array}$
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C. 24
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In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son?
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Solution(By Apex Team)
Let the average score of the remaining 6 batsmen be x runs. Then, sum of their scroe = 6x Captain’s score = (x + 30) ∴ 6x + (x + 30) = 310 ⇒ 7x = 280 ⇒ x = 40 Hence, captain’s score = x + 30 = 70
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Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average19 people went to a hotel for combine dinner party 13 by 8 runs. His new average is:
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A. 18
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$\begin{array}{l}\text{Let the number of paper be x}\\ \text{Then, pupil’s total score = 63x}\\ \begin{aligned}&\therefore\frac{63x+20+2}{x}=65\\ &\Rightarrow2x=22\\ &\Rightarrow x=11\end{aligned}\end{array}$
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D. 30
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Let the eight number be x Then, sixth number = (x – 7) Seventh number = (x – 7) + 4 = (x – 3) So, $\begin{aligned}&\Leftrightarrow\left(2\times15\frac{1}{2}\right)+\left(3\times21\frac{1}{2}\right)+(x-7)+(x-3)+x=8\times20\\ &\Leftrightarrow31+64+(3x-10)=160\\ &\Leftrightarrow3x=75\\ &\Leftrightarrow x=25\end{aligned}$
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Solution(By Apex Team)
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