ratio and proportion questions with solutions for competitive exams
Solve the following MCQ on ratio and proportion:
If A : B = \(\displaystyle \frac{1}{2}:\frac{3}{8}\), B : C = \(\displaystyle \frac{1}{3}:\frac{5}{9}\) and C : D = \(\displaystyle \frac{5}{6}:\frac{3}{4}\), then the ratio A : B : C : D is
(a) 6 : 4 : 8 : 10
(b) 6 : 8 : 9 : 10
(c) 8 : 6 : 10 : 9
(d) 4 : 6 : 8 : 10
(e) 6 : 8 : 10 : 12
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Answer: (c)
A : B =\(\displaystyle \frac{1}{2}:\frac{3}{8}\)= 4 : 3 = 8 : 6
B : C =\(\displaystyle \frac{1}{3}:\frac{5}{9}\)= 3 : 5 = 6 : 10
C : D =\(\displaystyle \frac{5}{6}:\frac{3}{4}\)= 10 : 9
Therefore, A : B : C : D = 8 : 6 : 10 : 9
If A : B : C = 2 : 3 : 4, then ratio \(\displaystyle \frac{A}{B}:\frac{B}{C}:\frac{C}{A}\) is equal to
(a) 8 : 9 : 16
(b) 8 : 9 : 12
(c) 8 : 9 : 24
(d) 4 : 9 : 16
(e) 5 : 9 : 14
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Answer: (c)
A : B : C = 2 : 3 : 4
\(\displaystyle \Rightarrow \) \(\displaystyle \frac{A}{B}=\frac{2}{3},\frac{B}{C}=\frac{3}{4},\frac{C}{A}=\frac{4}{2}=2\)
\(\displaystyle \Rightarrow \) \(\displaystyle \frac{A}{B}:\frac{B}{C}:\frac{C}{A}=\frac{2}{3}:\frac{3}{4}:\frac{2}{1}\)
= 8 : 9 : 24
If a : (b +c ) = 1 : 3 and c : (a + b ) = 5:7, then b : (a +c ) is equal to
(a) 1 : 2
(b) 2 : 3
(c) 1 : 3
(d) 2 : 1
(e) 3 : 1
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Answer: (a)
a : (b +c ) = 1 : 3
\(\displaystyle \Rightarrow \) \(\displaystyle \frac{{b+c}}{a}=\frac{3}{1}\) Þ \(\displaystyle \frac{{b+c}}{a}+1=\frac{3}{1}+1\)
\(\displaystyle \frac{{a+b+c}}{a}=\frac{{3+1}}{1}=\frac{4}{1}\) ….. (i)
Similarly, \(\displaystyle \frac{{a+b}}{c}=\frac{7}{5}\)
\(\displaystyle \Rightarrow \) \(\displaystyle \frac{{a+b+c}}{c}=\frac{{12}}{5}\) …..(ii)
On dividing (i) by (ii),
\(\displaystyle \frac{c}{a}=\frac{{4\times 5}}{{12}}=\frac{5}{3}=k\) ….. (iii)
From equation (i), b = 4k
\(\displaystyle \frac{b}{{a+c}}=\frac{{4k}}{{3k+5k}}=1:2\)
If p : q : r = 1 : 2 : 4, then \(\displaystyle \sqrt{{5{{p}^{2}}+{{q}^{2}}+{{r}^{2}}}}\) is equal to
(1) 5
(2) 2q
(3) 5p
(4) 4r
(e) 3q
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The Ratio and Proportion questions answer is (b)
\(\displaystyle \frac{p}{1}=\frac{q}{2}=\frac{r}{4}=k\)
\(\displaystyle \Rightarrow \) p = k , q = 2k , r = 4k
\(\displaystyle \sqrt{{5{{p}^{2}}+{{q}^{2}}+{{r}^{2}}}}=\sqrt{{5{{k}^{2}}+4{{k}^{2}}+16{{k}^{2}}}}=\sqrt{{25{{k}^{2}}}}\)
= 5k = 5p
The mean proportional between \(\displaystyle (3+\sqrt{2})and(12-\sqrt{{32}})\) is
(a) \(\displaystyle \sqrt{7}\)
(b) \(\displaystyle 2\sqrt{7}\)
(c) 6
(d) \(\displaystyle \frac{{15-3\sqrt{2}}}{2}\)
(e) 5
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Answer for this MCQ on Ratio and Proportion is (b)
Mean proportional = \(\displaystyle \sqrt{{(3+\sqrt{2})(12-\sqrt{{32}})}}\)
= \(\displaystyle \sqrt{{(3+\sqrt{2})4(3-\sqrt{2})}}\)
= \(\displaystyle 2\sqrt{{9-2}}=2\sqrt{7}\)
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