Maths Average Problems Short Tricks  Average short Tricks औसत शॉर्ट ट्रिक्स
Introduction:
Average (औसत) :
Sums of data divided by the number of items in the data will give the mean average. The mean average is used quite regularly to determine final math marks over a term or semester. Averages are often used in sports: batting averages which means number of hits to number of times at bat. Gas mileage is determined by using averages.
Average = Sum of Amounts / Number of amounts
Average = Sum of Amounts / Number of amounts
Formulas:
If A,B,C,D and E are five sum, then there average will be (A+4) or (E4)
similarly if there is six subsequently , then there average will be (A+5) or (E5).
Example :The average of five subsequently numbers A,B,C,D and E is 21. then find the mean of E.
Most Important Questions (Asked in Exam)
Previous year question of Average based problems
 
Ex. 1.

Nine persons went to a hotel for taking their meals. Eight of them spent Rs 12 each on their meals and the ninth spent Rs. 8 more than the average expenditure of all the nine. What was the total money spent by them?
9 लोग खाना खाने के लिए होटल मे गए। 8 लोगो ने 12 रुपे दिये और नोवे ने 8 रुपे ज्यादा दिये उनके एव्रेज से। कुल कितने रुपेए खर्चा हुआ

Sol.

Let the average expenditure of all the nine be Rs. x.
Then, 12 x 8 + (x + 8) = 9x or 8x = 104 or x = 13.
Total money spent = 9x = Rs. (9 x 13) = Rs. 117.

Ex. 2.

Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, find the largest number.
3 नुंबरों मे दूसरा पहले का दोगुना और तीसरे से तीन गुना है । यदि उन तीनों का औसत 44 हे ; तो सबसे बड़ा नंबर ज्ञात करो।

Sol.

Let the third number be x Then, second number = 3x. First number = 3x/2
x+3x+(3x/2) =(44x3) or = 44x3 or x = 24.
So, largest number = 2nd number = 3x = 72.

Ex. 3.

The average of 25 results is 18. The average of first twelve of them is 14 and that of last twelve is 17. Find the thirteenth result.
25 बचो के रिज़ल्ट का औसत 18 हे; उनमे से पहले 12 का औसत 14 हे तथा आखरी 12 का औसत 17 हे । 13 वे का रिज़ल्ट ज्ञात करो

Sol.

Clearly, thirteenth result = (sum of 25 results) — (sum of 24 results)
= (l8x25)[(14X12)+(17x12)]
= 450—(168+204) = 450—372
= 78.

Ex. 4.

The average of 11 results is 60. If the average of first six results is 58 and that of the last six is 63, find the sixth result.
11 रिज़ल्ट का औसत 60 है उनमे से पहले 6 का औसत 58 हे ठठा आखरी 6 का औसत 63 है 6ते का औसत ज्ञात करो ।

sol

Sixth result = (58 x 6 + 63 x 6 — 60 x 11)
= 66.

Ex. 5

The average weight of A, B, C is 45kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, find the weight of B.
A, B, C का औसात वजन 45 kg है। यदि A व B का औसत 40kg है तथा B व C का औसत वजन 43kg हो तो B का वजन बताए

Sol.

Let A, B and C represent their individual weights. Then,
A + B +C =(45 x3)kg= 135kg.
A+B = (40x2) kg = 80Kg
and B+C = (43x2)kg = 86kg
B =(A + B)+(B + C)—(A + B+ C) =(80 + 86—135) kg =31 kg.

Ex. 6.

The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
एक कक्षा के 39 बचो की उम्र का औसत 15 साल हे । यदि टीचर की उम्र भी जोड़ दी जाए तो उनका औसत 3 महीने बाद जाता है । टीचर की उम्र बताए

Sol

Total age of 39 persons = (39 x 15) years = 585 years.
Average age of 40 persons = 15 years 3 months = 61/3 years.
Total age of 40 persons = (61/3 x 40) years = 610 years.
Age of the teacher = (610 — 585) years = 25 years.

Ex. 7

The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new man.

Sol.

Total weight increased = (1.8 x 10) kg = 18 kg.
Weight of the new man (53 + 18) kg = 71 kg.

Ex. 8.

There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Ra. 42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?

Sol.

Let the original average expenditure be Rs. x Then,
42 (x — 1) — 35x = 42
7x = 84
x = 12.
:. Original expenditure = Rs. (35 x 12) = Rs. 420.

Ex. 9.

A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
एक खिलाड़ी ने 17वी पारी मे 87 रन बनाने के बाद उसका औसत 3 से बाद जाता है। उसका 17वी परी के बाद का औसत ज्ञात करो ।

Sol.

Let the average after 17th inning = x.
Then, average after 16th inning = (x — 3).
l6(x—3)+87=17x
0r x=(8748)
=39.

Ex. 10

Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour Find the average speed of the train during the whole journey.
दो स्टेशन के बीच की दूरी 778km है। एक रेलगाड़ी A से B की तरफ 84km प्रति घंटे तथा वापस 56 km प्रति घंटे से आती हे । रेल गाड़ी की औसत चाल ज्ञात करो ।

Sol.

Required average speed = (2xy/(x+y)) km/hr
=(2x84x56)/(84+56) km/hr
=(2x84x56)/140 km/hr
= 67.2 km/hr

Type and Average short Tricks 2:
The age of n peoples increase or decrease by X years. When a person whose age is Y years is replaced by another person, then age of that new person = (Y + nX) years or (Y  nX) years.
Example : The average weight of 6 persons increased by 1 kg. When a person whose weight is 45 kg is replaced by a new person. Find the weight of new person.
Type and Average short Tricks 3:
The age of n peoples increase or decrease by X years. When two person whose age is Y years and Z years are replaced by other persons, then average age of new persons = (Y +Z nX)/2 years or (Y +Z+ nX)/2 years
Example : In the group of 8 persons , two persons whose age is 25 years and 35 years are replaced by two other ladies, due to which the average age of group is increased by 1.5 years. find the average age of that two ladies.
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Type and Average short Tricks 4:
If average age of n people is X years , from that m peoples whose average age is Y years leave and new people come in there place whose average is Z years , then now average age of n people:= X  [{m(YZ)} / n] years
Example : In a class there are 40 students those average height is 145 cm. 8 students whose average height is 142 cm leave the class and other 8 students come in there place whose average height is 147 cm. now find the average height of the class.
Type and Average short Tricks 5:
If from n numbers, average of first (n1) numbers is X and average of last (n1) numbers is Y, then:
First number  Last number = (n1)(XY)
Example : From 4 numbers, average of first 3 numbers is 15 and average of last 3 numbers is 16. If last number is 19, then what will be the first number?
Type and Average short Tricks 6:
If average of n results is X and from that average of first m results is Y and last m numbers is Z , then :
 m th result = m(Y+Z)  nX
 (m+1) result = nX  m(Y+Z)
Example : Average of 13 results is 42. If average of first 7 results is 44 and last 7 numbers is 43 , then what will be the 7th result?
Type and Average short Tricks 7:
If any two things travels with 2 different speed X km/hour and Y km/hour and they travels 2 same distance , then average speed for hole travel = 2XY / (X+Y) km/hour
Example : A ship travels with 10 km/hour speed to a particular distance and returns with 15 km/hour speed. Find the average speed of hole distance.
Type and Average short Tricks 8:
If average age of G1 persons is A1 and average age of G2 persons is A2 and a=G2 and difference of G2 and b=A1 and difference of A2, then by the epl of figure:
Case 1. If (G1>G2 and A1>A2) or (G1<G2 and A1<A2), then average age of a persons:
= {(G1 x b) + (a x A2)} / a years
Case 2. If (G1>G2 and A1<A2) or (G1<G2 and A1>A2), then average age of a persons:
= {(G1 x b and a x difference of A2) / a} years
Example : In a class average age of 40 students is 15 years. 0.2 years increased due to entry of two new students. Find the average age of new students.
Type and Average short Tricks 9:
If average age of G1 persons is A1 , average age of G2 persons is A2 and average age of (G1+G2) is A, then:
G1 / (AA2) = G2 / (A1A) or G1 (A1A) = G2 (AA2)
Example : In a workshop average salary of all employs is 950 rs. If average salary of 15 employs is 5250 rs and average salary of other employs is 850 rs, then Find the number of other employs.
Type and Average short Tricks 10:
If out of three numbers, first number is n1 times of second number and second number is n2 times of third number, then:
Example : Average of three numbers is 49. If first number is twice of second number and second number is twice of third number, then find the difference between smallest and biggest number.
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