Question

Sum of 4 consecutive even numbers is 81 more than the sum of 3 consecutive odd numbers, sum of last even and odd number is 59. Find the difference between largest even and largest odd numbers?

Answer 1

Let x be an odd number
So consecutive odd numbers are x,x+2,x+4
Consecutive even numbers are x+1, x+3, x+5,x+7
According to the Problem,
Sum of even numbers = 81+ sum of odd numbers x+1+x+3+x+5+x+7=81+x+x+2+x+44x+16
= 3x+87x= 87 - 16
= 71
Odd  numbers are 71(x), 73(x+2), 75(x+4)
Even numbers are 72(x+1), 74(x+3), 76(x+5), 78(x+7)
the largest odd number is 75
the largest even number is 78
The difference between them is 78-75 
                                                   = 3 (ans)