Practice MCQ Questions and Answer on Chain Rule

1.

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) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Persons 6}}:9 \hfill \\ {\text{Working hours 8}}:6 \hfill \\ \end{gathered} \right\}::8400:x\] $$\eqalign{ & \therefore {\text{ }}6 \times 8 \times x = 9 \times 6 \times 8400 \cr & \Leftrightarrow x = \frac{{\left( {9 \times 6 \times 8400} \right)}}{{\left( {6 \times 8} \right)}} \cr & \Leftrightarrow x = 9450 \cr} $$

2.

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

• (A) 4
• (B) 9
• (C) 12
• (D) 49

Show Answer

 Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) $$\eqalign{ & \therefore 14:6::21:x \cr & \Rightarrow 14 \times x = 6 \times 21 \cr & \Rightarrow x = \frac{{6 \times 21}}{{14}} \cr & \Rightarrow x = 9 \cr} $$

3.

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

4.

If $$\frac{4}{9}$$ th of a bucket is filled in 1 minute, the rest of it will be filled in ?

• (A) $${\text{ 1 minute}}$$
• (B) $$\frac{9}{4}{\text{ minute}}$$
• (C) $$\frac{5}{4}{\text{ minute}}$$
• (D) $$\frac{4}{5}{\text{ minute}}$$

Show Answer

 Remaining part $$\eqalign{ & = \left( {1 - \frac{4}{9}} \right) \cr & = \frac{5}{9}{\text{ }} \cr} $$ Let the required time be x minutesMore volume to be filled , More time taken (Direct proportion) $$\eqalign{ & \therefore {\text{ }}\frac{4}{9}:\frac{5}{9}::1:x \cr & \Rightarrow \frac{4}{9}x = \frac{5}{9} \cr & \Rightarrow x = \left( {\frac{5}{9} \times \frac{9}{4}} \right) \cr & \Rightarrow x = \frac{5}{4}{\text{ }} \cr} $$

5.

A garrison had provision for a certain number of days. After 10 days, $$\frac{1}{5}$$ of the men desert and it is found that the provisions will now last just as long as before. How long was that ?

• (A) 15 days
• (B) 25 days
• (C) 35 days
• (D) 50 days

Show Answer

 Initially, Let there be x men having food for y days After 10 days, x men had food for days (y - 10) Also, $$\left( {x - \frac{x}{5}} \right)$$   men had food for y days $$\eqalign{ & \therefore \,x\left( {y - 10} \right) = \frac{{4x}}{5} \times y \cr & \Leftrightarrow 5xy - 50x = 4xy \cr & \Leftrightarrow xy - 50x = 0 \cr & \Leftrightarrow x\left( {y - 50} \right) = 0 \cr & \Leftrightarrow y - 50 = 0 \cr & \Leftrightarrow y = 50 \cr} $$

6.

If 5 men or 7 women can earn Rs. 5250 per day, how much would 7 men and 13 women earn per day ?

• (A) Rs. 11600
• (B) Rs. 11700
• (C) Rs. 16100
• (D) Rs. 17100

Show Answer

 Let the required earning be Rs. x 5 men = 7 women 7 men = $$ \left( \frac{7}{5} \times 7 \right) $$   women = $$\frac{49}{5}$$ women ∴ (7 men and 13 women) $$\eqalign{ & = \left( {\frac{{49}}{5} + 13} \right){\text{women}} \cr & = \frac{{114}}{5}{\text{ women}} \cr} $$ Now, More women, More earning (Direct proportion) $$\eqalign{ & \therefore {\text{ }}7 : \frac{{114}}{5}::{\text{ 5}}250 : x \cr & \Leftrightarrow 7x = \left( {\frac{{114}}{5} \times 5250} \right) \cr & \Leftrightarrow 7x = 119700 \cr & \Leftrightarrow x = 17100 \cr} $$

7.

15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, 3 women do as much work as 2 men ?

• (A) 18
• (B) 20
• (C) 25
• (D) 30

Show Answer

 3 women ≡ 2 men So, 21 women ≡ 14 men Less men, More days (Indirect proportion) Less hours per day, More days (Indirect proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 14}}:15 \hfill \\ {\text{Hours per day 6}}:8 \hfill \\ \end{gathered} \right\}::21:x\] $$\eqalign{ & \therefore \,\left( {14 \times 6 \times x} \right) = \left( {15 \times 8 \times 21} \right) \cr & \Leftrightarrow x = \frac{{\left( {15 \times 8 \times 21} \right)}}{{\left( {14 \times 6} \right)}} \cr & \Leftrightarrow x = 30 \cr} $$ ∴ Required number of days = 30

8.

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) \[\left. \begin{gathered} {\text{Length 100}}:600 \hfill \\ \,\,{\text{Women 40}}:10 \hfill \\ \end{gathered} \right\}::10:x\] $$\eqalign{ & \therefore {\text{ }}100 \times 40 \times x = 600 \times 10 \times 10 \cr & \Leftrightarrow x = \frac{{\left( {600 \times 10 \times 10} \right)}}{{\left( {100 \times 40} \right)}} \cr & \Leftrightarrow x = 15 \cr} $$

9.

20 men complete one-third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?

• (A) 10
• (B) 12
• (C) 15
• (D) 20

Show Answer

 Let the total number of men be x Work done = $$\frac{1}{3}$$ Remaining work = $$\left( {1 - \frac{1}{3}} \right) = \frac{2}{3}$$ More work, More men (Direct proportion) More days, Less men (Indirect proportion) \[\left. \begin{gathered} \,{\text{Work }}\frac{1}{3}:\frac{2}{3} \hfill \\ {\text{Days 25}}:20 \hfill \\ \end{gathered} \right\}::20:x\] $$\eqalign{ & \therefore {\text{ }}\left( {\frac{1}{3} \times 25 \times x} \right) = \left( {\frac{2}{3} \times 20 \times 20} \right) \cr & \Leftrightarrow x = \frac{{800}}{{25}} \cr & \Leftrightarrow x = 32 \cr} $$ ∴ More men to be employed = (32 - 20) = 12

10.

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 $$\eqalign{ & = \frac{{24}}{{4 \times 12}} \times 20 \cr & = {\text{Rs}}{\text{.10}} \cr} $$