Answer for this MCQ on Ratio and Proportion is (b)

Given , \(\displaystyle \frac{x}{y}=\frac{2}{3}\) ….. (i)

Expression = \(\displaystyle \frac{{3x+2y}}{{9x+5y}}\)

\(\displaystyle \frac{{3\frac{x}{y}+2}}{{9\frac{x}{y}+5}}=\frac{{3\times \frac{2}{3}+2}}{{9\times \frac{2}{3}+5}}\)   [from (i)]

= \(\displaystyle \frac{{2+2}}{{11}}=\frac{4}{{11}}\)

The Ratio and Proportion questions answer is (c)

a : b : c = 2 : 3 : 4

\(\displaystyle \frac{a}{2}=\frac{b}{3}=\frac{c}{4}=k\) (let)

\(\displaystyle \Rightarrow \) a = 2k, b = 3k, and c = 4k

Given 2a – 3b + 4c = 33

\(\displaystyle \Rightarrow \)2 × 2k –3×3k + 4 ×4k = 33

\(\displaystyle \Rightarrow \) 4k –9k + 16k = 33

\(\displaystyle \Rightarrow \) 11k = 33 Þ \(\displaystyle k=\frac{{33}}{{11}}=3\)

Therefore, c = 4k = 4×3 = 12

Answer: (d)

a : b : c = 7 : 3 : 5

\(\displaystyle \Rightarrow \frac{a}{7}=\frac{b}{3}=\frac{c}{5}=k\) (let)

\(\displaystyle \Rightarrow \)a = 7k, b = 3k, c = 5k

Now, (a + b + c) : (2a + b – c)

= (7k + 3k + 5k) : (2 ×7k +3k –5k)

= 15 k : 12 k = 5 : 4

Answer: (d)

According to the question,

2A = 3B

\(\displaystyle \Rightarrow \)  B = \(\displaystyle \frac{2}{3}\) A

and 2A = 4C

\(\displaystyle \Rightarrow \)  C = \(\displaystyle \frac{1}{2}\) A

Therefore,

A : B : C = A : \(\displaystyle \frac{2}{3}\) : \(\displaystyle \frac{1}{2}\) A

= 1 : \(\displaystyle \frac{2}{3}\) A : \(\displaystyle \frac{1}{2}\)

= 6 : 4  : 3

Answer: (b)

A : B = 3 : 4 = 9 : 12

B : C = 12 : 13

Therefore, A : B : C = 9 : 12 : 13

\(\displaystyle \Rightarrow \) A : C = 9 : 13

Alternately :

A : C = xp : yq

= 3 × 12 : 4 × 13

= 9 : 13