Solution: We have to find the number of apples did Mandy sell on the \(10^{th}\) day.

Given: Mandy sold 600 apples in 10 days and the number of apples she sold increased by 4 each day

\(1^{st}\) day: x

\(2^{nd}\) day: x + 4

\(3^{rd}\) day: x + 4 + 4 = x + 2 * 4 .
.
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\(10^{th}\) day: x + 9 * 4

=> x + (x + 4) + (x + 2 * 4) + ….+(x + 9 * 4) = 600

=> 10 x + 4 + 2 * 4 + …..+ 9 * 4 = 600

=> 10x + 4( 1 + 2 + …. + 9) = 600

=> 1 + 2 + 3 + 4 +…..+ n = \(\frac{n\left(n+1\right)}{2}\)

=> 10x + 4[\(\frac{9\cdot10}{2}\)] = 600

=> 10x + 180 = 600

=> 10x = 420

=> x = 42

=> ∴ \(10^{th}\) day = x + 9*4 = 42 + 36 = 78

Therefore, D is the correct answer.

Answer D