consider the ratio 12:5 if this ratio has to be reduced by 20% which common number should be added to both the numerator and denominator?
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Consider
12/5. This has to be reduced by 20%. This means we have to consider 80% of this number. (Why?) Thus we must get
We have to find a such that
12+ a / 5+ a = 48/25
.
Cross multiplying, we obtain
25(12+a)=48(5+a).
This simplifies to
48a−25a=(25×12)−(48×5), or 23a=60.
Hence,
a= 60/23
If we add 60/23 to both terms of 12:5 we get a ratio which is 20% less than the original ratio.
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