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RATIO AND PROPORTION
SIMPLE PROBLEMS
1.If a:b =5:9 and b:c=4:7 Find a:b:c?
Sol: a:b=5:9 and b:c=4:7=4*9/4:9*4/9=9:63/9
a:b:c=5:9:63/9=20:36:63
2.Find the fourth proportion to 4,9,12
Sol: d is the fourth proportion to a,b,c
a:b=c:d
4:9=12:x
4x=9*12=>x=27
3.Find third proportion to 16,36
Sol: if a:b=b:c then c is the third proportion to a,b
16:36=36:x
16x=36*36
x=81
4.Find mean proportion between 0.08 and 0.18
Sol: mean proportion between a and b=square root of ab
mean proportion =square root of 0.08*0.18=0.12
5.If a:b=2:3 b:c=4:5, c:d=6:7 then a:b:c:d is
Sol: a:b=2:3 and b:c=4:5=4*3/4:5*3/4=3:15/4
c:d=6:7=6*15/24:7*15/24=15/4:35/8
a:b:c:d=2:3:15/4:35/8=16:24:30:35
6.2A=3B=4C then A:B:C?
Sol: let 2A=3B=4C=k then
A=k/2, B=k/3, C=k/4
A:B:C=k/2:k/3:k/4=6:4:3
7.15% of x=20% of y then x:y is
Sol: (15/100)*x=(20/100)*y
3x=4y
x:y=4:3
8.a/3=b/4=c/7 then (a+b+c)/c=
Sol: let a/3=b/4=c/7=k
(a+b+c)/c=(3k+4k+7k)/7k=2
9.Rs 3650 is divided among 4 engineers, 3 MBA’s and 5 CA’s such that 3 CA’s get as much as 2 MBA’s and 3 Eng’s as much as 2 CA’s .Find the share of an MBA.
Sol: 4E+3M+5C=3650
3C=2M, that is M=1.5C
3E=2C that is E=.66 C
Then, (4*0.66C)+(3*1.5C)+5C=3650
C=3650/12.166
C=300
M=1.5 and C=450.
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