At first, Box F had 18 pears and 42 lemons while Box G had 36 pears and 50 lemons. Then, some lemons were moved from Box F to Box G and some pears were moved from Box G to Box F. In the end, Box F contained pears and lemons in the ratio 3:4 while
(a) In the end, how many lemons were in Box F?
(b) In the end, how many more pears did Box G contain than Box F?
+1694 Your "challenging question" is incomplete!!! 
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At first, Box F had 18 pears and 42 lemons while Box G had 36 pears and 50 lemons. Then, some lemons were moved from Box F to Box G and some pears were moved from Box G to Box F. In the end, Box F contained pears and lemons in the ratio 3:4 while Box G contained pears and lemons in the ratio 1:2.
(a) In the end, how many lemons were in Box F?
(b) In the end, how many more pears did Box G contain than Box F?
Here
At first, Box F had 18 pears and 42 lemons while Box G had 36 pears and 50 lemons. Then, some lemons were moved from Box F to Box G and some pears were moved from Box G to Box F. In the end, Box F contained pears and lemons in the ratio 3:4 while Box G contained pears and lemons in the ratio 1:2
(a) In the end, how many lemons were in Box F?
(b) In the end, how many more pears did Box G contain than Box F?
P==Pears, L==Lemons
[18 + P] / [42 - L] ==3 /4,
[36 - P] / [50 + L] ==1/2, solve for A, B
L==10, P==6
Box F ==18 + 6=24 pears
==42 - 10=32 lemons
Box G ==36 - 6 ==30 pears
==50 + 10=60 lemons.
(a) - In the end, there were ==32 Lemons in Box F
(b) - In the end, there were: 30 - 24 ==6 more Pears in Box G than Box F
