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The average of eight numbers is 25, that of the first two is 20 and of the next three is 26. The sixth number is less than the seventh by 4, and less than the eighth by 6. The last number is

  • a)
    30

  • b)
    32

  • c)
    40

  • d)
    36

Correct answer is option 'A'. Can you explain this answer?
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The average of eight numbers is 25, that of the first two is 20 and of...
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Most Upvoted Answer
The average of eight numbers is 25, that of the first two is 20 and of...
Total of 8 numbers 25* 8=200

First two numbers 20*2 = 40

Next three. 26*3 = 78

Last three 200–40–78 = 82


6th number x

7th number x+4

8th number x+ 6

x+x+4+x+6 = 3x+10 =82

x = 24

Last number = x+6 = 30
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Community Answer
The average of eight numbers is 25, that of the first two is 20 and of...
Given information:
- Average of eight numbers = 25
- Average of first two numbers = 20
- Average of next three numbers = 26
- Sixth number is less than seventh by 4 and eighth by 6

To find: The last number

Solution:
Let's denote the eight numbers by a, b, c, d, e, f, g, h.

1. Average of eight numbers = 25
a + b + c + d + e + f + g + h = 25 x 8 = 200

2. Average of first two numbers = 20
a + b = 20 x 2 = 40

3. Average of next three numbers = 26
c + d + e = 26 x 3 = 78

4. Sixth number is less than seventh by 4 and eighth by 6
f = g - 4
f = h - 6

From equation 4, we can write:
g - 4 = h - 6
g = h - 2

Substituting this value of g in equation 1, we get:
a + b + c + d + e + f + (h - 2) + h = 200
a + b + c + d + e + f + 2h = 202

Substituting values from equations 2 and 3 in the above equation, we get:
40 + 78 + f + 2h = 202
f + 2h = 84

Substituting the value of f from equation 4, we get:
(g - 4) + 2h = 84
Substituting the value of g from above, we get:
(h - 6) + 2h = 84
3h = 90
h = 30

Therefore, the last number is 30.

Hence, the correct option is (a) 30.
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