Practice MCQ Questions and Answer on Chain Rule

21.

If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day ?

• (A) 1260
• (B) 1320
• (C) 920
• (D) 1380

Show Answer

 Let the required number of chairs be x Then, More carpenters, More chairs (Direct proportion) More hours per day, More chairs (Direct proportion) More days, More chairs (Direct proportion) \[\left. \begin{gathered} \,\,\,\,{\text{Carpenters 12}}:18 \hfill \\ {\text{Hours per day 6}}:8 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 24}}:{\text{36}} \hfill \\ \end{gathered} \right\}::460:x\] $$\eqalign{ & \therefore {\text{ }}12 \times 6 \times 24 \times x = 18 \times 8 \times 36 \times 460 \cr & \Leftrightarrow x = \frac{{\left( {18 \times 8 \times 36 \times 460} \right)}}{{\left( {12 \times 6 \times 24} \right)}} \cr & \Leftrightarrow x = 1380 \cr} $$ ∴ Required number of chairs = 1380

22.

The cost of 21 pencils and 9 clippers is Rs. 819. The cost price of 7 pencils and 3 clippers is = ?

• (A) Rs. 204
• (B) Rs. 409
• (C) Rs. 273
• (D) Rs. 208

Show Answer

 Cost of 21 pencils and 9 clippers = Rs. 819 Cost of 7 pencils and 3 clippers = $$\frac{{819}}{3}$$ = Rs. 273

23.

The work done by a women in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work, working 8 hours per day ?

• (A) $$\text{1}\frac{1}{2}\text{ days}$$
• (B) $$\text{3 days}$$
• (C) $$\text{3}\frac{2}{3}\text{ days}$$
• (D) $$\text{4}\frac{1}{2}\text{ days}$$

Show Answer

 Ratio of time taken by a woman, a man and a boy $$\eqalign{ & = 8:6:12 \cr & = 4:3:6 \cr} $$ So, 4 women ≡ 3 men ≡ 6 boy (12 mens + 12 womens + 12 boys) $$\eqalign{ & = \left[ {12 + \left( {\frac{3}{4} \times 12} \right) + \left( {\frac{3}{6} \times 12} \right)} \right]{\text{men}} \cr & {\text{ = }}\left( {12 + 9 + 6} \right){\text{men}} \cr & = 27{\text{ men}} \cr} $$ Let the required number of days be x More men, Less days (Indirect proportion) More working hours, Less days (Indirect proportion) \[\left. \begin{gathered} {\text{Working hours 8}}:6 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Men 27}}:9 \hfill \\ \end{gathered} \right\}::6:x\] $$\eqalign{ & \therefore \,27 \times 8 \times x = 9 \times 6 \times 6 \cr & \Leftrightarrow x = \frac{{\left( {9 \times 6 \times 6} \right)}}{{\left( {27 \times 8} \right)}} \cr & \Leftrightarrow x = \frac{3}{2} \cr & \Leftrightarrow x = 1\frac{1}{2} \cr} $$

24.

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) $$\eqalign{ & \therefore {\text{ }}\frac{4}{9}:\frac{5}{9}::1:x \cr & \Rightarrow \frac{4}{9}x = \frac{5}{9} \cr & \Rightarrow x = \left( {\frac{5}{9} \times \frac{9}{4}} \right) \cr & \Rightarrow x = \frac{5}{4}{\text{ }} \cr} $$

25.

A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day than was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job ?

• (A) 8 days
• (B) 9 days
• (C) 10 days
• (D) 12 days

Show Answer

 Let the team take x days to finish 360 pieces Then, number of pieces made each day = $$\frac{{360}}{x}$$ More number of pieces per day, Less days (Indirect proportion) $$\eqalign{ & \therefore \,\left( {\frac{{360}}{x} + 4} \right):\frac{{360}}{x}::x:\left( {x - 1} \right) \cr & \Leftrightarrow \left( {\frac{{360}}{x} + 4} \right) \left( {x - 1} \right) = \frac{{360}}{x} \times x \cr & \Leftrightarrow 360 - \frac{{360}}{x} + 4x - 4 = 360 \cr & \Leftrightarrow 4x - \frac{{360}}{x} - 4 = 0 \cr & \Leftrightarrow x - \frac{{90}}{x} - 1 = 0 \cr & \Leftrightarrow {x^2} - x - 90 = 0 \cr & \Leftrightarrow \left( {x - 10} \right)\left( {x + 9} \right) = 0 \cr & \Leftrightarrow x = 10 \cr} $$

26.

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) $$\eqalign{ & \therefore {\text{ }}7 : \frac{{114}}{5}::{\text{ 5}}250 : x \cr & \Leftrightarrow 7x = \left( {\frac{{114}}{5} \times 5250} \right) \cr & \Leftrightarrow 7x = 119700 \cr & \Leftrightarrow x = 17100 \cr} $$

27.

30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers to finish the same piece of work in 30 days, will be ?

• (A) 15
• (B) 21
• (C) 22
• (D) 25

Show Answer

 Let the required number of labourers be x Less working hour/day, More labours (Indirect proportion) More days, Less labourers (Indirect proportion) \[\left. \begin{gathered} {\text{Working hours/day 6}}:7 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 30}}:18 \hfill \\ \end{gathered} \right\}::30:x\] $$\eqalign{ & \therefore 6 \times 30 \times x = 7 \times 18 \times 30 \cr & \Leftrightarrow 6x = 126 \cr & \Leftrightarrow x = 21 \cr} $$

28.

In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

• (A) 20
• (B) 30
• (C) 40
• (D) 50

Show Answer

 There is a meal for 200 children 150 children have taken the meal Remaining meal is to be catered to 50 children Now,200 children = 120 men ∴ 50 children $$\eqalign{ & = \left( {\frac{{120}}{{200}} \times 50} \right){\text{men}} \cr & = {\text{30 men}} \cr} $$

29.

A snapshot $$\text{1}\frac{7}{8}\times 2\frac{1}{2}$$   is to be enlarged so that the longer dimension is 4. What will be the dimension of the shorter side ?

• (A) $$\text{2}\frac{3}{8}$$
• (B) $$\text{2}\frac{1}{2}$$
• (C) $$\text{3}$$
• (D) $$\text{3}\frac{3}{8}$$

Show Answer

 Let the dimension of the shorter side be x More is the longer side, More is the shorter side (Direct proportion) $$\eqalign{ & \therefore 2\frac{1}{2}:4::1\frac{7}{8}:x \cr & \Leftrightarrow \frac{5}{2}x = 4 \times \frac{{15}}{8} \cr & \Leftrightarrow x = \left( {\frac{{15}}{2} \times \frac{2}{5}} \right) \cr & \Leftrightarrow x = 3 \cr} $$

30.

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) $$\eqalign{ & \therefore 42:56::24:x \cr & \Leftrightarrow 42 \times x = 56 \times 24 \cr & \Leftrightarrow x = \left( {\frac{{56 \times 24}}{{42}}} \right) \cr & \Leftrightarrow x = 32 \cr} $$