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The average of four numbers is 140. The fourth number is 26 more than the first number and the third number is 18 more than the second number. If the second number is 18 more than the first number, then what is the difference between third and fourth number?

The average of four numbers is 140. The fourth number is 26 more than the first number and the third number is 18 more than the second number. If the second number is 18 more than the first number, then what is the difference between third and fourth number? Correct Answer 10

Let the four numbers be ‘X1’, ‘X2’, ‘X3’ and ‘X4’ respectively.

From the question ∶

(X1 + X2 + X3 + X4)/4 = 140

X1 + X2 + X3 + X4 = 560      ----(1)

Given that,

X4 = X1 + 26

And, X3 = X2 + 18

From equation (1) ∶

X1 + X2 + (X2 + 18) + (X1 + 26) = 560

2X1 + 2X2 = 560 – 44 = 516

X1 + X2 = 258 ---- (2)

Also given that, X2 – X1 = 18      ----(3)

From (2) and (3) ∶

X2 = 138, X1 = 138 – 18 = 120

So, X4 = 120 + 26 = 146

And X3 = 138 + 18 = 156

Required difference = 156 – 146 = 10

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