The average weight of first 11 persons among 12 persons is 95 kg. The weight of 12th person is 33 kg more than the average weight of all the 12 persons. The weight of the 12th person is
(1) 128.75 kg
(2) 128 kg
(3) 131 kg
(4) 97.45 kg
Answer: (3)
Let the weight of 12th person = x kg
Average weight of 12 persons =\(\displaystyle \frac{{11\times 95+x}}{{12}}\) kg
According to the question,
\(\displaystyle \begin{array}{l}\frac{{11\times 95+x}}{{12}}+33=x\\\Rightarrow 1045+x+396=12x\\\Rightarrow 1441=11x\\x=\frac{{1441}}{{11}}=131\end{array}\)
The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted from the last number the average be[1]comes 17.5 then the number of natural number is
(1) 15
(2) 30
(3) 20
(4) 10
Answer: (4)
Number of natural numbers = x
Their sum = 15x
According to the question,
\(\displaystyle \begin{array}{l}15x+30-5=x\times 17.5\\\Rightarrow 17.5x-15x=25\\\Rightarrow 2.5x=25\\\Rightarrow x=\frac{{25}}{{2.5}}=10\end{array}\)
The average of five numbers is 49. The average of the first and the second numbers is 48 and the average of the fourth and fifth numbers is 28. What is the third number?
(a) 92
(b) 91
(c) 95
(d) Cannot be determined
(e) None of these
Answer: (e)
Sum of five numbers = 5 \(\displaystyle \times \) 49 = 245
Sum of first and second numbers = 2 \(\displaystyle \times \) 48 = 96
Sum of fourth and fifth numbers = 2 \(\displaystyle \times \) 48 = 56
Third number = 245 \(\displaystyle -\) 152 = 93
or
Third number = 5 \(\displaystyle \times \) 49 \(\displaystyle -\) 2 \(\displaystyle \times \) 48 \(\displaystyle -\) 2 \(\displaystyle \times \) 28
= 245 \(\displaystyle -\) 96 \(\displaystyle -\) 56 = 93
Alternate method
Average of 5 no’s =49
Therefore, sum of 5 no’s = 5 \(\displaystyle \times \)49 =245
Average of first and second Number =48
Therefore, sum of first and second Number = 2 \(\displaystyle \times \) 48 =96
Average of 4th and 5th number = 28
Therefore, sum of 4th and 5th Number =2 \(\displaystyle \times \)28 = 56
Let the third number =x
Sum of 5 numbers = 96+x+56
Therefore,
96+x+56 =245
x+152=245
x = 245 \(\displaystyle -\) 152
x=93
The average of five numbers is 57.8. The average of the first and the second numbers is 77.5 and the average of the fourth and fifth numbers is 46. What is the third number?
The average speed of a bus is 8 times the average speed of a bike. The bike covers a distance of 186 km in 3 hours. How much distance will the bus cover in 10 hours?
(a) 4069 km
(b) 4096 km
(c) 4960 km
(d) 4690 km
(e) None of these
Answer: (c)
Speed of bike = \(\displaystyle \frac{{Dis\tan ce}}{{Time}}=\frac{{186}}{3}=62kmph\)
\(\displaystyle \Rightarrow \)Speed of bus = 8 × 62 = 496 kmph
Distance covered by bus in 10 hours = 496 × 10 = 4960 km
