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Average of s numbers is 16 and fous of thenumbers are 12, le 16 and is find the fourthnumbers |
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Answer» LET the four numbers be a ,b,c,d The average of first 3 of 4 numbers is 16 average = \frac{\TEXT{Sum of first three numbers}}{3}average= 3 Sum of first three numbers
16 = \frac{a+b+c}{4}16= 4 a+b+c
16 \times 3 =a+b+c16×3=a+b+c 48 =a+b+c48=a+b+c ---1 The avg. of last 3 number is 14 average = \frac{\text{Sum of last three numbers}}{3}average= 3 Sum of last three numbers
14 = \frac{a+b+c+d}{4}14= 4 a+b+c+d
14 \times 3 =b+c+d14×3=b+c+d 42 =b+c+d42=b+c+d ---2 The sum of first and last number is 16 a+d=16 ---3 Substitute the VALUE of a from 3 in 1 48 =16-d+b+c48=16−d+b+c 32= -d+b+c32=−d+b+c --- 4 Add 2 and 4 42+32=b+c+d+b+c-d 74=2(b+c) b+c= 37 Substitute the value of b+c in 1 48 =a+3748=a+37 48-37 =a48−37=a 11=a11=a Substitute the value of a in 3 11+d=16 d=16-11 d=5 Hence last no is 5 |
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