Average & Percentage BY: MAYANK AGNIHOTR
SOME BASIC FORMULAS Average: Average Sum of observations Number of observations Percentage Concept of Percentage: By a certain percent, we mean that many hundredths Thus, x percent means x hundredths, written as x%. To express x% as a fraction: We have, x% = 100 To express a as percent: we have a = (a 100 Ex : 1-6 x 100) 96-2096 )%
Results on Population: Let the population of a town be P now and suppose it increases at the rate of R% per annum, then 1. Population after n years- P1+ 0 2. Population n years ago . 100
Questions Ques 1. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. Find the monthly income of P Sol Let P, Q and R represent their respective monthly incomes. Then, we have P+Q (5050 x 2) 10100.. ) Q R (6250 x 2) 12500.. (ii) P R (5200 x 2) 10400) Adding (i), (i) and (ii), we get: 2(P Q+R) 33000 or P+Q+ R 16500 Subtracting (ii) from (iv), we get P 4000 P's monthly income Rs. 4000. iv)
Ques 2. A library has an average of 510 visitors on Sundays and 240 on other days. Find the average number of visitors per day in a month of 30 days beginning with a Sunday Since the month begins with a Sunday, to there will be five Sundays in the month No. of visitor on Sunday 510 x 5 &No. of visitor on other day 240 x 25 Sol. 510x5+240x25 8550 285 Ans Required average- A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets? Ques 3. Sol. Number of runs made by running 110 (3 x 4 8 x 6) -110 (60) -50 Required %- (110x 100) %245 % Ans
Ques 4, A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had how many apples Sol Suppose originally he had x apples Then, (100-40=60)90 of x 420. 60 xx=420 x=700 Ans 100 5 Ques 5. A student multiplied a number by g instead of . What is the percentage error in the calculation? So. Let the no. be x Then error = 5x-3x = 16x 3 15 Error % = (-5x) 100 % = 16 100 = 6490 Ans 15 5
Population of a town increases at the rate of 10% pa. Present population is 10000 find population after 3 years Ques 6. 3 So Population after 3 years 10101013310 Ans 1+1 ). 10000 11. 13310 Ans 13310 Ans = 100 100 100
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