FACTS AND FORMULAE FOR AVERAGE QUESTIONS
1. Average =
2. Suppose a man covers a certain distance x kmph and an equal distance at y kmph. Then, the average speed during the whole journey isKmph
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).
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?
Let the average after 7th inning = x
Then average after 16th inning = x - 3
16(x-3)+87 = 17x
x = 87 - 48 = 39
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 ?
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8
The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
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