Practice MCQ Questions and Answer on Chain Rule

51.

If 5 spiders can catch five files in five minutes, how many files can hundred spiders catch in 100 minutes ?

• (A) 100
• (B) 500
• (C) 1000
• (D) 2000

Show Answer

 Let the required number of chairs be x. Then, More spiders, More flies (Direct proportion) More time, More flies (Direct proportion) \[\left. \begin{gathered} \,\,\,{\text{Spiders 5}}:100 \hfill \\ {\text{Minutes 5}}:100 \hfill \\ \end{gathered} \right\}::5:x\] $$\eqalign{ & \therefore {\text{ }}5 \times 5 \times x = 100 \times 100 \times 5 \cr & \Leftrightarrow x = \frac{{\left( {100 \times 100 \times 5} \right)}}{{\left( {5 \times 5} \right)}} \cr & \Leftrightarrow x = 2000 \cr} $$

52.

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

• (A) 1
• (B) $$\frac{1}{{40}}$$
• (C) 40
• (D) 80

Show Answer

 Let the required number of days be x. Less cows, More days (Indirect Proportion) Less bags, Less days (Direct Proportion) \[\left. \begin{gathered} {\text{Cows}}\,\,\,\,\,1:40 \hfill \\ {\text{Bags}}\,\,\,\,\,40:1 \hfill \\ \end{gathered} \right\}::40:x\] $$\eqalign{ & \therefore 1 \times 40 \times x = 40 \times 1 \times 40 \cr & \Rightarrow x = 40 \cr} $$

53.

The cost of 8 fans and 14 ovens is Rs. 36520. What is the cost of 12 fans and 21 ovens ?

• (A) Rs. 56800
• (B) Rs. 54780
• (C) Rs. 57950
• (D) Cannot be determined

Show Answer

 Cost of 8 fan's and 14 oven's is Rs. 36520 Cost of 4 fan's and 7 oven's is Rs. $$\frac{{{\text{36520}}}}{2}$$  = Rs.18260 Cost of 12 fan's and 21 oven's is = 18260 × 3 = Rs. 54780

54.

The cost of 4 dozen papers is Rs. 24. The cost of 1 score of papers (in rupees) is ?

• (A) 40
• (B) 20
• (C) 10
• (D) 42

Show Answer

 1 score of papers = 20 papers Cost of 4 dozen papers = Rs.24 Cost of 20 papers $$\eqalign{ & = \frac{{24}}{{4 \times 12}} \times 20 \cr & = {\text{Rs}}{\text{.10}} \cr} $$

55.

A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the food lasts for 35 days longer, the number of men originally in the fort were ?

• (A) 2500
• (B) 3000
• (C) 3500
• (D) 4000

Show Answer

 Let there be x men originally So, x men had provisions 40 days whereas (x + 500) men consumed it in 35 days More men, Less days (Indirect proportion) $$\eqalign{ & \therefore \,\left( {x + 500} \right):x::40:35 \cr & \Leftrightarrow 35 \times \left( {x + 500} \right) = 40x \cr & \Leftrightarrow 5x = 35 \times 500 \cr & \Leftrightarrow x = \left( {\frac{{35 \times 500}}{5}} \right) \cr & \Leftrightarrow x = 3500 \cr} $$

56.

If 5 workers can collect 60 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

• (A) 80 kg
• (B) 100 kg
• (C) 120 kg
• (D) 160 kg

Show Answer

 Let the required quantity be x kg. More workers, More quantity (Direct proportion) More days, More quantity (Direct proportion) \[\left. \begin{gathered} {\text{Workers 5}}:8 \hfill \\ \,\,\,\,\,\,\,\,{\text{Days 3}}:5 \hfill \\ \end{gathered} \right\}::60:x\] $$\eqalign{ & \therefore {\text{ }}5 \times 3 \times x = 8 \times 5 \times 60 \cr & \Leftrightarrow x = \frac{{\left( {8 \times 5 \times 60} \right)}}{{\left( {5 \times 3} \right)}} \cr & \Leftrightarrow x = 160 \cr} $$

57.

56 men can complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work ?

• (A) 18
• (B) 32
• (C) 48
• (D) 98

Show Answer

 Let the required number of days be x Less men, More days (Indirect proportion) $$\eqalign{ & \therefore 42:56::24:x \cr & \Leftrightarrow 42 \times x = 56 \times 24 \cr & \Leftrightarrow x = \left( {\frac{{56 \times 24}}{{42}}} \right) \cr & \Leftrightarrow x = 32 \cr} $$

58.

49 pumps can empty a reservoir in $$6\frac{1}{2}$$ days, working 8 hours a day. If 196 pumps are used for 5 hours each day, then the same work will be complete in ?

• (A) 2 days
• (B) $${\text{2}}\frac{1}{2}$$ days
• (C) $${\text{2}}\frac{3}{5}$$ days
• (D) 3 days

Show Answer

 Let the required number of days be x Then, More pumps, Less days (Indirect proportion) Less working hour/day, More days (Indirect proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\ {\text{Working hour/day 5}}:8 \hfill \\ \end{gathered} \right\}::\frac{{13}}{2}:x\] $$\eqalign{ & \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr & \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr & \Leftrightarrow x = \frac{{13}}{5} \cr & \Leftrightarrow x = 2\frac{3}{5} \cr} $$

59.

3 pumps , working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day ?

• (A) 9
• (B) 10
• (C) 11
• (D) 12

Show Answer

 Let the required number of working hours per day be x More pumps, Less working hours per day (Indirect proportion) Less days, More working hours per day (Indirect proportion) \[\left. \begin{gathered} {\text{Pumps 4}}:3 \hfill \\ \,\,\,\,\,\,{\text{Days 1}}:2 \hfill \\ \end{gathered} \right\}::8:x\] $$\eqalign{ & \therefore {\text{ }}4 \times 1 \times x = 3 \times 2 \times 8 \cr & \Leftrightarrow x = \frac{{\left( {3 \times 2 \times 8} \right)}}{{\left( 4 \right)}} \cr & \Leftrightarrow x = 12 \cr} $$

60.

If 6 persons working 8 hours a day earn Rs. 8400 per week, then 9 persons working 6 hours a day will earn per week ?

• (A) Rs. 8400
• (B) Rs. 9450
• (C) Rs. 16200
• (D) Rs. 16800

Show Answer

 Let the weekly earning be Rs. xMore persons , More earning (Direct proportion) Less working hours, Less earning (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Persons 6}}:9 \hfill \\ {\text{Working hours 8}}:6 \hfill \\ \end{gathered} \right\}::8400:x\] $$\eqalign{ & \therefore {\text{ }}6 \times 8 \times x = 9 \times 6 \times 8400 \cr & \Leftrightarrow x = \frac{{\left( {9 \times 6 \times 8400} \right)}}{{\left( {6 \times 8} \right)}} \cr & \Leftrightarrow x = 9450 \cr} $$