ratio and proportion questions for bank exams with solutions
Solve the following MCQ on ratio and proportion:
₹ 6200 divided into three parts proportional to \(\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{5}\) are respectively
(a) ₹ 3000, ₹ 2000, ₹ 1200
(b) ₹ 3500, ₹ 1500, ₹ 1200
(c) ₹ 2500, ₹ 2000, ₹ 1700
(d) ₹ 2200, ₹ 3000, ₹ 1000
(e) ₹ 2400, ₹ 3200, ₹ 1500
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The Ratio and Proportion questions answer is (a)
Ratio = \(\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{5}\)
= \(\displaystyle \frac{1}{2}\times 30:\frac{1}{3}\times 30:\frac{1}{5}\times 30\)
= 15 : 10 : 6
Sum of the ratios = 15 + 10 + 6 = 31
Therfore, First part = \(\displaystyle \frac{{15}}{{31}}\times 6200=3000\)
Second part = \(\displaystyle \frac{{10}}{{31}}\times 6200=2000\)
Third part = \(\displaystyle \frac{6}{{31}}\times 6200=1200\)
94 is divided into two parts in such a way that the fifth part of the first and the eighth part of the second are in the ratio 3 : 4. The first part is :
(a) 30
(b) 36
(c) 40
(d) 28
(e) 32
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Answer: (a)
First part = x and second part = 94 – x
Therefore, \(\displaystyle \frac{{\frac{x}{5}}}{{\frac{{94-x}}{8}}}=\frac{3}{4}\)
\(\displaystyle \frac{x}{5}\times \frac{8}{{(94-x)}}=\frac{3}{4}\)
\(\displaystyle \Rightarrow \) 32 x = 15 × 94 – 15x
\(\displaystyle \Rightarrow \) 47 x = 15 × 94
x = \(\displaystyle \frac{{15\times 94}}{{47}}=30\)
If a : b = 5 : 7 and c : d = 2a : 3b , then ac : bd is :
(a) 20 : 38
(b) 50 : 147
(c) 10 : 21
(d) 50 : 151
(e) 55 : 251
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Answer: (b)
\(\displaystyle \frac{a}{b}=\frac{5}{7},\frac{c}{d}=\frac{{2a}}{{3b}}\)
\(\displaystyle \frac{a}{b}\times \frac{c}{d}=\frac{5}{7}\times \frac{{2a}}{{3b}}\)
\(\displaystyle \frac{{ac}}{{bd}}=\frac{{10}}{{21}}\times \frac{5}{7}=\frac{{50}}{{147}}=50:147\)
If x : y = 3 : 2, then the ratio \(\displaystyle 2{{x}^{2}}+3{{y}^{2}}:3{{x}^{2}}-2{{y}^{2}}\) is equal to :
(a) 12 : 5
(b) 6 : 5
(c) 30 : 19
(d) 5 : 3
(e) 4 : 7
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Answer: (c)
x : y = 3 : 2
\(\displaystyle {{x}^{2}}:{{y}^{2}}=9:4\)
\(\displaystyle \frac{{2{{x}^{2}}+3{{y}^{2}}}}{{3{{x}^{2}}-2{{y}^{2}}}}=\frac{{2\frac{{{{x}^{2}}}}{{{{y}^{2}}}}+3}}{{3\frac{{{{x}^{2}}}}{{{{y}^{2}}}}-2}}\)
= \(\displaystyle \frac{{2\times \frac{9}{4}+3}}{{3\times \frac{9}{4}-2}}=\frac{{\frac{{18+12}}{4}}}{{\frac{{27-8}}{4}}}=30:19\)
If a : b = b : c , then \(\displaystyle {{a}^{4}}:{{b}^{4}}\) is equal to
(a) \(\displaystyle ac:{{b}^{2}}\)
(b) \(\displaystyle {{a}^{2}}:{{c}^{2}}\)
(c) \(\displaystyle {{c}^{2}}:{{a}^{2}}\)
(d) \(\displaystyle {{b}^{2}}:ac\)
(e) \(\displaystyle {{b}^{2}}:{{c}^{2}}\)
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Answer for this MCQ on Ratio and Proportion is (b)
\(\displaystyle \frac{a}{b}=\frac{b}{c}\)
\(\displaystyle {{b}^{2}}=ac\) Þ \(\displaystyle {{b}^{4}}={{a}^{2}}{{c}^{2}}\)
\(\displaystyle \frac{{{{a}^{4}}}}{{{{b}^{4}}}}=\frac{{{{a}^{4}}}}{{{{a}^{2}}{{c}^{2}}}}=\frac{{{{a}^{2}}}}{{{{c}^{2}}}}\)
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