Quantitative Aptitude
CHAIN RULE MCQs
Total Questions : 326
| Page 28 of 33 pages
Answer: Option C. -> $${\text{2}}\frac{3}{5}$$ days
Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\
{\text{Working hour/day 5}}:8 \hfill \\
\end{gathered} \right\}::\frac{{13}}{2}:x\]
$$\eqalign{
& \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr
& \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr
& \Leftrightarrow x = \frac{{13}}{5} \cr
& \Leftrightarrow x = 2\frac{3}{5} \cr} $$
Let the required number of days be x
Then,
More pumps, Less days (Indirect proportion)
Less working hour/day, More days (Indirect proportion)
\[\left. \begin{gathered}
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\
{\text{Working hour/day 5}}:8 \hfill \\
\end{gathered} \right\}::\frac{{13}}{2}:x\]
$$\eqalign{
& \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr
& \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr
& \Leftrightarrow x = \frac{{13}}{5} \cr
& \Leftrightarrow x = 2\frac{3}{5} \cr} $$
Answer: Option B. -> 21
Let the required number of labourers be x
Less working hour/day, More labours (Indirect proportion)
More days, Less labourers (Indirect proportion)
\[\left. \begin{gathered}
{\text{Working hours/day 6}}:7 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 30}}:18 \hfill \\
\end{gathered} \right\}::30:x\]
$$\eqalign{
& \therefore 6 \times 30 \times x = 7 \times 18 \times 30 \cr
& \Leftrightarrow 6x = 126 \cr
& \Leftrightarrow x = 21 \cr} $$
Let the required number of labourers be x
Less working hour/day, More labours (Indirect proportion)
More days, Less labourers (Indirect proportion)
\[\left. \begin{gathered}
{\text{Working hours/day 6}}:7 \hfill \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 30}}:18 \hfill \\
\end{gathered} \right\}::30:x\]
$$\eqalign{
& \therefore 6 \times 30 \times x = 7 \times 18 \times 30 \cr
& \Leftrightarrow 6x = 126 \cr
& \Leftrightarrow x = 21 \cr} $$
Answer: Option B. -> $${\text{3}}\frac{3}{4}{\text{ days}}$$
Let the required number of days be x
3 men = 6 women
⇒12 men = (2 × 12) women = 24 women
∴ 12 men and 8 women = (24 + 8) women = 32 women
Now, More women, Less days (Indirect Proportion)
$$\eqalign{
& \therefore {\text{ }}32:6::20:x \cr
& \Leftrightarrow x = \left( {\frac{{6 \times 20}}{{32}}} \right) \cr
& \Leftrightarrow x = \frac{{15}}{4} \cr
& \Leftrightarrow x = 3\frac{3}{4} \cr} $$
Let the required number of days be x
3 men = 6 women
⇒12 men = (2 × 12) women = 24 women
∴ 12 men and 8 women = (24 + 8) women = 32 women
Now, More women, Less days (Indirect Proportion)
$$\eqalign{
& \therefore {\text{ }}32:6::20:x \cr
& \Leftrightarrow x = \left( {\frac{{6 \times 20}}{{32}}} \right) \cr
& \Leftrightarrow x = \frac{{15}}{4} \cr
& \Leftrightarrow x = 3\frac{3}{4} \cr} $$
Answer: Option A. -> 48 paise
Answer: Option D. -> Rs. 2500
Answer: Option A. -> 22.8 kg
Answer: Option D. -> Rs. 220
Answer: Option D. -> Rs. (yd/x)
Answer: Option D. -> 885.5 km
Answer: Option B. -> 195