Question

The average of 7 numbers is 25 that of first two is 23 and of the last two is 19. If the
3rd, 4th and 5th numbers bear a ratio of 1/ 4:1/2:1 to one another, what is 4" number?
b) 25
c) 26
e) None
a) 13
d) 50

Answer 1

26

Step-by-step explanation:

let the number be a, b, c, d, e, f, g

avg f first two is 23 [a+b]/2=23 a+b=46eq (1)

avg of last two is 19 {f+g}/2=19 f+g=38 eq (2)

from (1) and (2)

a+b=46

f+g=38

here the middle numbers in the ratio 1:2:4( by Simplifing)

(a+b+c+d+e+f+g) /7=25

a+b+c+d+e+f+g =175

46+x+2x+4x+38= 175

7x=91

x=13

fourth number(d) =2x

=2 into 13

=26

Answer 2

The 4th number is (c) 26.

Given:

The average of 7 numbers is 25

The average of the first two numbers is 23

The average of the last two numbers is 19

3rd, 4th and 5th numbers bear a ratio of 1/4 : 1/2: 1 to one another

To Find: The 4th number in the series.

Solution:

The total sum of the 7 numbers = 7 × 25

                                                       = 175

Now, average of any 2 numbers 'a' and 'b' is = (a+b)/2

So accordingly, sum of first 2 numbers = 23 × 2 = 46

Sum of last 2 numbers = 19 × 2 = 38                              

It is said that the 3rd, 4th and 5th numbers bear a ratio of 1/4: 1/2: 1 to one another, so we can write,

1/4 : 1/2 : 1 = k                        [ k is a positive constant ]

∴ 3rd number = 4k,

4th number = 2k, and

5th number = k.

So, the summation of all the numbers must be equal to the total sum calculated. According to the equation,

46 + 4k + 2k + k + 38 = 175

⇒ 7k = 91

⇒ k = 13

Hence the 4th number is = 2k = 2 × 13

                                            = 26

The 4th number is (c) 26

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