Delhi Police Constable Exam Model Paper 7

Question : 83 of 100

Marks: +1, -0

The average of six numbers is 40. If the average of first three numbers is 35. If fifth number is 5 more than the fourth number and sixth number is 10 more than the fourth number ; find fifth number?

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Solution:

Given:
The average of six numbers = 40
The average of first three numbers = 35
The fifth number is 5 more than the fourth number and sixth number is 10 more than the fourth number
Concept:
If average of N numbers is x, then total sum of N numbers = Nx
Calculation:
The average of six numbers = 40
⇒ Total sum of 6 numbers

= 6 × 40 = 240

The average of first three numbers = 35
⇒ Total sum of first 3 numbers

= 3 × 35 = 105

∴ Total sum of

4^{th}, 5^{th},

and

6^{th}

numbers

= 240 - 105 = 135

Let x be the

4^{th}

number,

5^{th}

number = x + 5

6^{th}

number = x + 10
Now,
Total sum of

4^{th}

5^{th}

, and

6^{th}

numbers

= x + (x + 5) + (x + 10) = 135⇒ 3x + 15 = 135

⇒

3x = 120

∴ x = 40

5^{th}

number

= x + 5 = 40 + 5 = 45

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