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If a:b=5:2, then (a+b):(aтИТb)=?
7 : 3
3 : 7
5 : 2
2 : 5
7 : 3
Since the ratio is given, directly substitute a = 5 and b = 2 into the expression. The constant k cancels out, so (5+2) / (5-2) gives the result instantly.
The ratio of two variables a and b is given as a : b = 5 : 2.
aтИТba+bтАЛ=k(aratioтАЛ)тИТk(bratioтАЛ)k(aratioтАЛ)+k(bratioтАЛ)тАЛ
Since the ratio is given, directly substitute a = 5 and b = 2 into the expression. The constant k cancels out, so (5+2) / (5-2) gives the result instantly.
Students often mistakenly calculate (a-b) / (a+b) or invert the values of a and b, resulting in an incorrect ratio like 3:7 instead of 7:3.
Define the ratio variables
Assume a=5k and b=2k, where k is a non-zero constant.
a=5k,b=2k
Substitute into the required expression
Substitute the values of a and b into the expression aтИТba+bтАЛ.
aтИТba+bтАЛ=5kтИТ2k5k+2kтАЛ
Simplify the expression
Combine the terms in the numerator and denominator and cancel out the common constant k.
3k7kтАЛ=37тАЛ
A is correct because substituting a = 5 and b = 2 into the expression results in 7 : 3.
This substitution method is the foundation for solving complex problems in Mixture and Alligation, where ratios are frequently converted into absolute values using a constant factor.
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