type 1 basic concepts of ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts
ratio & proportion PRACTICE TEST [9 - EXERCISES]
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
Question : 11 [SSC CPO S.I.2006]
If x : y = 2 : 3, then the value of ${3x+ 2y}/{9x+ 5y}$ is equal to
a) $1/2$
b) $5/14$
c) $4/11$
d) $11/4$
Answer »Answer: (c)
Given, $x/y = 2/3$ ... (i)
Expression = ${3x + 2y}/{9x + 5y}$
= ${3x/y + 2}/{9x/y+ 5} = {3×2/3+2}/{9×2/3+5}$[from (i)]
= ${2 + 2}/11 =4/11$
Question : 12 [SSC CPO S.I.2006]
The mean proportional between $(3 +√2)$ and $(12 - √32)$ is
a) 6
b) ${15 -3√2}/2$
c) $2√7$
d) $√7$
Answer »Answer: (c)
Using Rule 14Mean Proportion - Let x be the mean proportion between a and b, then a:x::x:b (Real condition)$a/x = x/b ⇒ x^2 =ab$$x =√{ab}$So, mean proportion of a and b = $√{ab}$If x be the mean proportion between (x - a) and (x - b) then what will be the value of x ?$x = {ab}/{a+b}$
Mean proportional
=$√{(3+√2)(12-√{32})}$
= $√{(3+√2)4(3-√2)}$
= 2$√{9 - 2} = 2√7$
Question : 13 [SSC SO 2006]
If a, b, c are three numbers such that a : b = 3 : 4 and b : c = 8 : 9, then a : c is equal to
a) 3 : 2
b) 1 : 2
c) 2 : 3
d) 1 : 3
Answer »Answer: (c)
We can write a : c by compounding a : b and b : c
$a/c = a/b × b/c, a/c = 3/4 × 8/9, a/c =2/3$
a : c = 2 : 3
Using Rule 18If A:B = x:y and B:C = p:q then(i) A:C = xp : yq(ii) A:B:C = (x:y) × p:qy =xp:yp:qy It is done as follows:A:B = x:y B:C = p:qA:B:C = xp:yp:qy
A : C = xp : yq
= 3 × 8 : 4 × 9 = 2 : 3
Question : 14 [SSC CPO S.I.2006]
If a : (b+c) = 1 : 3 and c : (a+ b) = 5:7, then b : (a+c) is equal to
a) 1 : 3
b) 2 : 1
c) 2 : 3
d) 1 : 2
Answer »Answer: (d)
a : (b+c) = 1: 3
${b+ c}/a = 3/1 ⇒ {b+c}/a+1 =3/1$+1
${a+ b + c}/a= {3+1}/1 = 4/1$ ... (i)
Similarly, ${a + b}/c = 7/5$
${a + b + c}/c = 12/5$ ... (ii)
On dividing (i) by (ii),
$c/a = {4 × 5}/12 = 5/3$ =k ... (iii)
From equation (i), b = 4k
$b/{a + c} = {4k}/{3k + 5k} =1 : 2$
Question : 15 [SSC CGL Prelim 2005]
If a : b = b : c, then $a^4 : b^4$ is equal to
a) $c^2 : a^2$
b) $b^2$ : ac
c) $a^2 : c^2$
d) ac : $b^2$
Answer »Answer: (c)
$a/b = b/c$
$b^2 = ac ⇒ b^4 = a^2c^2$
$a^4/b^4 = a^4/{a^2c^2} = a^2/c^2$
IMPORTANT quantitative aptitude EXERCISES
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199+ Ratio Proportion Basic Concepts MCQ Questions Answers »
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Top 199+ Ratio Proportion Age Based MCQ Questions Answers »
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159+ Ratios Proportions Addition Subtraction product MCQ »
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199+ Ratio Proportion Income, Expenditure Problems MCQS »
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199+ Partnership Aptitude (Ratio) MCQ Questions Answers »
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259+ Ratio and Proportion (fractions) Aptitude MCQ Quiz »
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199+ Ratio and Proportion Aptitude Questions Answers MCQ »
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299+ Alligation and Mixture Problems Aptitude MCQ Quiz »
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249+ Ratio and Proportion Coins Based Questions Answers »
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