Question

the average of first 3 of 4 numbers is 16 and avg of last 3 number is 14 sum of first and last number is 16 .find last no

Answer 1

last no. = 5

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Answer 2

Answer:

5

Step-by-step explanation:

Let the four numbers be a ,b,c,d

The average of first 3 of 4 numbers is 16

$average = \frac{\text{Sum of first three numbers}}{3}$

$16 = \frac{a+b+c}{4}$

$16 \times 3 =a+b+c$

$48 =a+b+c$ ---1

The avg. of last 3 number is 14

$average = \frac{\text{Sum of last three numbers}}{3}$

$14 = \frac{a+b+c+d}{4}$

$14 \times 3 =b+c+d$

$42 =b+c+d$ ---2

The sum of first and last number is 16

a+d=16 ---3

Substitute the value of a from 3 in 1

$48 =16-d+b+c$

$32= -d+b+c$  --- 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

$48 =a+37$

$48-37 =a$

$11=a$

Substitute the value of a in 3

11+d=16

d=16-11

d=5

Hence  last no is 5