Practice MCQ Questions and Answer on Chain Rule

1.

21 binders can bind 1400 books in 15 days. How many binders will required to bind 800 books in 20 days ?

• (A) 7
• (B) 9
• (C) 12
• (D) 14

Show Answer

 Let the required number of binders be x Less books, Less binders (Direct proportion) More days, Less binders (Indirect proportion) \[\left. \begin{gathered} {\text{Books 1400}}:800 \hfill \\ \,\,\,\,\,\,\,\,\,{\text{Days 20}}:15 \hfill \\ \end{gathered} \right\}::21:x\] $$\eqalign{ & \therefore {\text{ }}1400 \times 20 \times x = 800 \times 15 \times 21 \cr & \Leftrightarrow x = \frac{{\left( {800 \times 15 \times 21} \right)}}{{\left( {1400 \times 20} \right)}} \cr & \Leftrightarrow x = 9 \cr} $$

2.

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) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Pumps 196}}:49 \hfill \\ {\text{Working hour/day 5}}:8 \hfill \\ \end{gathered} \right\}::\frac{{13}}{2}:x\] $$\eqalign{ & \therefore {\text{ }}196 \times 5 \times x = 49 \times 8 \times \frac{{13}}{2} \cr & \Leftrightarrow x = \left( {49 \times 8 \times \frac{{13}}{2} \times \frac{1}{{196 \times 5}}} \right) \cr & \Leftrightarrow x = \frac{{13}}{5} \cr & \Leftrightarrow x = 2\frac{3}{5} \cr} $$

3.

A wall of 100 meters can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 metres ?

• (A) 15
• (B) 20
• (C) 25
• (D) 30

Show Answer

 Let the required number of days be x 7 men = 10 women (14 men and 20 women) = (20 + 20) women = 40 women More length, More days (Direct proportion) More women, Less days (Indirect proportion) \[\left. \begin{gathered} {\text{Length 100}}:600 \hfill \\ \,\,{\text{Women 40}}:10 \hfill \\ \end{gathered} \right\}::10:x\] $$\eqalign{ & \therefore {\text{ }}100 \times 40 \times x = 600 \times 10 \times 10 \cr & \Leftrightarrow x = \frac{{\left( {600 \times 10 \times 10} \right)}}{{\left( {100 \times 40} \right)}} \cr & \Leftrightarrow x = 15 \cr} $$

4.

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

5.

Running at the same constant rate, 6 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce on 30 minutes ?

• (A) 225
• (B) 250
• (C) 300
• (D) 350

Show Answer

 Let the required number of bottles be x More machines, More bottles produced (Direct proportion) Less time, Less bottles produce (Direct proportion) \[\left. \begin{gathered} {\text{Machines 6}}:15 \hfill \\ \,\,\,\,\,\,{\text{Times 60}}:30 \hfill \\ \end{gathered} \right\}::180:x\] $$\eqalign{ & \therefore {\text{ }}6 \times 60 \times x = 15 \times 30 \times 180 \cr & \Leftrightarrow x = \frac{{\left( {15 \times 30 \times 180} \right)}}{{\left( {6 \times 60} \right)}} \cr & \Leftrightarrow x = 225 \cr} $$

6.

If 5 engines consume 6 metric tonnes of coal when each is running 9 hours a day, how many metric tonnes of coal will be needed for 8 engines, each running 10 hours a day, it begin given that 3 engines of the former type consume as much as 4 engines of the latter type ?

• (A) $$\text{3}\frac{1}{8}$$
• (B) 8
• (C) $$\text{8}\frac{8}{9}$$
• (D) $$\text{6}\frac{12}{25}$$

Show Answer

 Let the required quantity of coal be x metric tonnes More engines, More coal (Direct proportion) More hours per day, More coal (Direct proportion) More rate, More coal (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Engines 5}}:8 \hfill \\ {\text{Hours per day 9}}:10 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Rate }}\frac{1}{3}:\frac{1}{4} \hfill \\ \end{gathered} \right\}::6:x\] $$\eqalign{ & \therefore \,\,\left( {5 \times 9 \times \frac{1}{3} \times x} \right) = \left( {8 \times 10 \times \frac{1}{4} \times 6} \right) \cr & \Leftrightarrow 15x = 120 \cr & \Leftrightarrow x = 8 \cr} $$

7.

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) $$\eqalign{ & \therefore \,\left( {x + 500} \right):x::40:35 \cr & \Leftrightarrow 35 \times \left( {x + 500} \right) = 40x \cr & \Leftrightarrow 5x = 35 \times 500 \cr & \Leftrightarrow x = \left( {\frac{{35 \times 500}}{5}} \right) \cr & \Leftrightarrow x = 3500 \cr} $$

8.

A man completes $$\frac{5}{8}$$ of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

• (A) 5
• (B) 6
• (C) 7
• (D) $$7\frac{1}{2}$$

Show Answer

 $$\eqalign{ & {\text{Work}}\,{\text{done}} = \frac{5}{8} \cr & {\text{Balance}}\,{\text{work}} = {1 - \frac{5}{8}} = \frac{3}{8} \cr & {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{number}}\,{\text{of}}\,{\text{days}}\,{\text{be}}\,x \cr & {\text{Then}}, \cr &\frac{5}{8}:\frac{3}{8} :: 10:x \cr & \Rightarrow \frac{5}{8} \times x = \frac{3}{8} \times 10 \cr & \Rightarrow x = {\frac{3}{8} \times 10 \times \frac{8}{5}} \cr & \Rightarrow x = 6 \cr} $$

9.

A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm ?

• (A) 40
• (B) 49
• (C) 100
• (D) None of these

Show Answer

 Let the required number of rounds be x More radius, Less rounds (Indirect proportion) $$\eqalign{ & \therefore {\text{ }}20:14::70:x \cr & \Leftrightarrow \left( {20 \times x} \right) = \left( {14 \times 70} \right) \cr & \Leftrightarrow x = \frac{{\left( {14 \times 70} \right)}}{{20}} \cr & \Leftrightarrow x = 49 \cr} $$

10.

Four gardeners with four grass mowers mow 400 sq. m of ground in 4 hours. How long would it take for eight gardeners with eight grass mowers to mow 800 sq. m of ground ?

• (A) 4 hours
• (B) 6 hours
• (C) 8 hours
• (D) 12 hours

Show Answer

 Since each gardener would work with one grass mower, So, we shall consider 1 gardener and 1 grass mower as one unit. Let the required time be x hours More gardeners and grass mowers, Less time (Indirect proportion) More area, More time (Direct proportion) \[\left. \begin{gathered} {\text{Gardeners & grass mowers 8}}:4 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Area 400}}:800 \hfill \\ \end{gathered} \right\}::4:x\] $$\eqalign{ & \therefore {\text{ }}8 \times 400 \times x = 4 \times 800 \times 4 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 800 \times 4} \right)}}{{\left( {8 \times 400} \right)}} \cr & \Leftrightarrow x = 4 \cr} $$