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Question

# If twice the sum of 5 consecutive odd numbers and thrice the sum of 4 consecutive even numbers is 178 and thrice the sum of 5 consecutive odd numbers and twice the sum of 4 consecutive even numbers is 177, then the difference between the sum of 5 consecutive odd numbers and 4 consecutive even numbers is

A

1

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B

3

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C

5

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D

7

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Solution

## The correct option is A 1 Let the odd numbers be x,x+2,x+4,x+6 and x+8. Their Sum = 5x+20 Let the even numbers be y,y+2,y+4 and y+6. Their Sum = 4y+12 Given that: 2(5x+20)+3(4y+12)=178 and 3(5x+20)+2(4y+12)=177 Simplifying the above two equations, we get 5x+6y=51 ...(1) 15x+8y=93 ...(2) Multiplying (1) by 3, 15x+18y=153 ...(3) Subtracting (2) from (3), we get 10y=60⇒y=6 Substituting y=6 in (1), we get x=3. Therefore, the odd numbers are 3, 5, 7, 9, 11 and the even numbers are 6, 8, 10, 12. Arranging them in ascending order, the numbers are 3,5,6,7,8,9,10,11,12. The required difference = (6+8+10+12) - (3+5+7+9+11) = 1

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