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Examples

June 3, 2020
Category: Examples

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Examples :

(1) Find the average of first 7 prime numbers.

Soln. Required average = $\left (\frac{2+3+5+7+11+13+17}{7} \right )$ = $\left (\frac{58}{7} \right )$ = 8.29

(2) Find the average of first 20 multiples of 7.

Soln. First multiple = 7 and 20^th multiple = 140.

( Also first 20 multiples of 7 are in A.P. )

$\therefore \textup{ } \overline{x}$ = $\frac{7+140}{2}$ = $\frac{147}{2}$ = 73.5

(3) The average weight of a class of 49 students is 35 kg. If the weight of the teacher be included, the average rises by 500 gms. Find the weight of the teacher.

Soln. The weight of teacher = 35.5 kg. + 500 gms. $\times$ 49 students

( Due to teacher each student’s weight

is increased by 500 gms. )

= 35.5 kg. + 24500 gms.

= 35.5 kg. + 24.5 kg.

= 60 kg.

(4) A batsman makes a score of 300 runs in the 26^th inning and thus increased his average by 10. Find his average after 26^th inning.

Soln. Due to 300 runs his average increased by 10 runs.

i.e. due to 300 runs his runs ( in each of 26 innings ) 10 runs are increased.

His old average = 300 – ( 26 $\times$ 10 )

= 300 – 260

= 40 runs

Hence, its new average ( after 26^th inning ) = 40 + 10 = 50 runs.

(5) A man covers a distance from a town A to a town B on scooter at 60 km per hour and rides back from B to A at 40 km per hour. Find his average speed during the whole journey.

Soln. Average speed = $\left (\frac{2ab}{a+b} \right )$ km/hr. = $\frac{2\times 60\times 40}{60+40}$ km/hr. = 48 km/hr.

(6) The average temperature for Monday, Tuesday and Wednesday was 50 ⁰ C. The average for Tuesday, Wednesday and Thursday was 51 ⁰ C. If the temperature on Thursday be 35 ⁰ C, find the temperature on Monday.

Soln M + T + W = 3 $\times$ 50

= 150 ––––––– ( 1 )

T + W + Th = 3 $\times$ 51

= 153 ––––––– ( 2 )

Subtracting equation (1) from equation (2), we get

Th – M = 3

$\therefore$ 35 – M = 3

$\therefore$ 35 – 3 = M

$\therefore$ M = 32

Hence, the temperature on Monday = 32 ⁰ C

(7) The average of 21 results is 100. If the average of first 11 results is 98 and that of last 11 is 101, find the 11^th result.

Soln. Sum of 21 results = ( 21 $\times$ 100 ) = 2100 –––––––– (1)

Sum of first 11 results = (11 $\times$ 98) = 1078 ––––––– (2)

Sum of last 11 results = (11 $\times$ 101) = 1111 ––––––– (3)

Adding equation (1) and (2), we get

Sum of 21 results + 11^th result = 2189 –––––––– (4)

Subtracting equation (1) from (4), we get

$\therefore$ 11^th result = ( 2189 – 2100 ) = 89.

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