0 vote
The average of 28 numbers 79 . The average of first 14 number is 76 and average of last 15 number is 84 . If 14th number is excluded then what is average of remaining number.
The average of 28 numbers 79 . The average of first 14 number is 76 and average of last 15 number is 84 . If 14th number is excluded then what is average of remaining number.
$77.97$
$74.77$
$77.77$
$79.45$
1 answers
0 vote
MATHS MIRROR APPROACH
76 is 3 less than 79, it means 14 numbers can give its 3 numbers i,e., 14 ÃÂ -3 = -52 to the needy. Similarly 84 is 5 more than 79 it means 15 numbers need 5 numbers ie., 5 ÃÂ 15 = 75 more. So, 14 numbers can give its 3 to 15 numbers. Therefore, Extra needed = 75 - 52 = 33.As we know that 14th number is taken twice when we combine first 14 and last 15 numbers so we can understand that the value of extra needed is 14th number.When 14th number is removing then it will take its value from the remaining (27) numbers.Average of remaining 27 numbers = 79 - $\frac{33}{27}$ = 77.77
BASIC APPROACH -As first 14 + last 15 = 29 numbers but the total numbers are 28. Also last number of first 14 numbers and first number of last 15 numbers is 14th number so we can easily understand that the 14th number is counted twice.Value of 14th number $=$ (sum of first 14 numbers + Sum of last 15 numbers) $-$ sum of 28 number
$=14$ th number $=(14 \times 76+15 \times 84-28 \times$ $79)$
$=(1064+1260-2212)$ $=112$
Average of remaining 27 number $=($ Sum of 28 number $-14$ th number $) \div 27$
$=2212-112=2100$
$=\frac{2100}{27}$
$=77.77$
76 is 3 less than 79, it means 14 numbers can give its 3 numbers i,e., 14 ÃÂ -3 = -52 to the needy. Similarly 84 is 5 more than 79 it means 15 numbers need 5 numbers ie., 5 ÃÂ 15 = 75 more. So, 14 numbers can give its 3 to 15 numbers. Therefore, Extra needed = 75 - 52 = 33.As we know that 14th number is taken twice when we combine first 14 and last 15 numbers so we can understand that the value of extra needed is 14th number.When 14th number is removing then it will take its value from the remaining (27) numbers.Average of remaining 27 numbers = 79 - $\frac{33}{27}$ = 77.77BASIC APPROACH -As first 14 + last 15 = 29 numbers but the total numbers are 28. Also last number of first 14 numbers and first number of last 15 numbers is 14th number so we can easily understand that the 14th number is counted twice.Value of 14th number $=$ (sum of first 14 numbers + Sum of last 15 numbers) $-$ sum of 28 number
$=14$ th number $=(14 \times 76+15 \times 84-28 \times$ $79)$
$=(1064+1260-2212)$ $=112$
Average of remaining 27 number $=($ Sum of 28 number $-14$ th number $) \div 27$
$=2212-112=2100$
$=\frac{2100}{27}$
$=77.77$
Other Questions
7. Name the British Governor General who started railways in India ?