There are 3 persons X, Y and Z. On some day, X lent tractors to Y and Z as
many as they had. After a month Y gave as many tractors to X and Z as many as
they have. After a month Z did the same thing. At the end of this transaction each
one of them had 24.
Find the tractors each originally had?
Answer
One way to solve it is by making 3 equations and solve them simultaneously. But
there is rather easier way to solve it using Backtracing.
It's given that at the end, each had 24 tractors (24, 24, 24) i.e. after Z gave
tractors to X & Y as many as they had. It means that after getting tractors from Z
their tractors got doubled. So before Z gave them tractors, they had 12 tractors
each and Z had 48 tractors. (12, 12, 48)
Similarly, before Y gave tractors to X & Z, they had 6 & 24 tractors respectively
and Y had 42 tractors i.e. (6, 42, 24)
Again, before X gave tractors to Y & Z, they had 21 & 12 tractors respectively
and X had 39 tractors i.e. (39, 21, 12)
Hence, initially X had 39 tractors, Y had 21 tractors and Z had 12 tractors.
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