Wednesday, 28 October 2015

Quantitative Shortcuts:Ratio and Fractions

Ratios-Important rules and shortcuts

Example:If P:Q=2:3, Q:R=4:5 then P:R=?
P/R=(P/Q)*(Q/R)=2/3*4/5=8/15,thus P:R=8:15

Example:P:Q:R=2:3:4,then P/Q:Q/R:R/P=?

Example:If 2P=3Q=4R then P:Q:R=?
Let 2P=3Q=4R=K, 
we get P=K/2,Q=K/3,R=K/4 
=> P:Q:R=K/2:K/3:K/4=1/2:1/3:1/4=6:4:3

Example:P:Q=1:2,Q:R=4:5,R:S=10:3 then P:Q:R:S=?
 Make the  Q term in first and second fraction same and make the R term similar in second and third fractions as follows


Comparison of ratios and Fractions

Method1:To compare two fractions  we can  make either denominators same or numerators same.
Example:2/5 and 3/10
To find out which is greater, make denominators same.We get 4/10 and 3/10.From this we can conclude,2/5>3/10
                            or make numerator same
Fractions will become 6/15 and 6/20,obviously 6/15>6/20.

Method2:This method can be applied if difference between numerator and denominator is same for all given fractions.
Example:1/2,3/4,7/8. Here 2-1=4-3=8-7=1.In such cases, just look at the numerator .Smaller the numerator will be smaller fraction.1/2<3 span="">

Method3:this method is applicable for all fractions.
If a/b and c/d are fractions under consideration,cross multiply numerator and denominator .ie a*d and c*b.
If a*d>b*c,then a/b>c/d

Example:7/11 and 3/5

cross multiply denominator and numerator.We get 7*5 and 11*3 

Since 7*5>11*3 ,7/11>3/5

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