This question is testing you on forming algebraic equations and solving it.
Let 4 a be the number of apples initially. Let 7 p be the number of pears initially.
(I chose to use 4 a and 7 p because of the fractions involved in the question)
Initially,
4 a = 7 p + 200 — (1)
After the fruit were sold,
Remaining apples left = 4 a x 3/4 = 3 a
Remaining pears left = 7 a x 5/7 = 5 p
Hence, 3 a = 5 p + 170 — (2)
(Now, with the 2 equations, you can solve for a and p.)
(Since 12 is the LCM of 3 and 4, I choose to multiply equation 1 by 3 and equation 2 by 4.)
(1) x 3:
12 a = 21 p + 600 — (3)
(2) x 4:
12 a = 20 p + 680 — (4)
(Using the substitution method, I can substitute equation 3 into equation 4.)
Sub (3) into (4):
21 p + 600 = 20 p + 680
p = 80
Sub p = 80 into (1)
(a) 4 a = 7 (80) + 200
= 760//
(b) 5 p = 5 (80)
= 400//