We look for a number between 25 and 55 which leaves a remainder of 3 when divided by 4 and which leaves a remainder of 4 when divided by 7.

Numbers which leave a remainder of 4 when divided by 7 are 4, 11, 18, 25, 32, 39, 46, 53, ...

Only 39 leaves a remainder of 3 when divided by 4.

So, Joshua bought 39 kg of apples.

Sir, Any algebraic expression to solve

Here algebraic approaches do not work, because the quotient concerned may not be the same number at all.

In our case, the quotients are 5 and 9 respectively, so this does not work.

Because if we were to use algebra, we get this

Eq 1 gives (x - 3) / 4 = whole number
Eq 2 gives (x - 4) / 7 = whole number

Both of which are probably not the same number, so you cannot equate them together.