Question

The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :

Answer 1

Let the 6 numbers be a,b,c,d,e, and f

Average =

Average = Sum of the data/Total no. of data

So, according to the Question ,

(a + b + c + d + e + f)/6 = 30

=> a + b + c + d + e + f = 180 ...eq.01

Now average of First Four Number is 25

=> ( a + b + c + d)/4 = 25

=> a + b + c + d = 100 ...eq.02

also given that average of last three numbers is 35

=> (d + e + f)/3 = 35

=> d + e + f = 105

=> e + f = 105 - d ...eq.03

In eq. 01,

a + b + c + d + e + f = 180

=> (a + b + c + d) + 105 - d = 180 (from eq.03)

=> 100 + 105 - d = 108 [from eq. 02]

=> 205 - d = 108

=> - d = - 97

=> d = 97

Hence the fourth number is 97 (ANS)

Answer 2

Step-by-step explanation:

Let the 6 numbers be a,b,c,d,e, and f

Average =

Average = Sum of the data/Total no. of data

So, according to the Question ,

(a + b + c + d + e + f)/6 = 30

=> a + b + c + d + e + f = 180 ...eq.01

Now average of First Four Number is 25

=> ( a + b + c + d)/4 = 25

=> a + b + c + d = 100 ...eq.02

also given that average of last three numbers is 35

=> (d + e + f)/3 = 35

=> d + e + f = 105

=> e + f = 105 - d ...eq.03

In eq. 01,

a + b + c + d + e + f = 180

=> (a + b + c + d) + 105 - d = 180 (from eq.03)

=> 100 + 105 - d = 108 [from eq. 02]

=> 205 - d = 108

=> - d = - 97

=> d = 97

Hence the fourth number is 97 (ANS)

hope this helps you!!