Practice MCQ Questions and Answer on Chain Rule

61.

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

• (A) 10
• (B) 13
• (C) 14
• (D) 15

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 Let the required number of days bex. Less persons, More days (Indirect Proportion) More working hours per day, Less days (Indirect Proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Persons }}\,30:39 \hfill \\ {\text{Working hour/day }}\,{\text{6}}:{\text{5}} \hfill \\ \end{gathered} \right\}::12:x\] $$\eqalign{ & \therefore 30 \times 6 \times x = 39 \times 5 \times 12 \cr & \Rightarrow x = \frac{{ {39 \times 5 \times 12} }}{{ {30 \times 6} }} \cr & \Rightarrow x = 13 \cr} $$

62.

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

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

63.

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

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

64.

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

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 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 $$\eqalign{ & = \left( {\frac{{120}}{{200}} \times 50} \right){\text{men}} \cr & = {\text{30 men}} \cr} $$

65.

4 persons can prepare an admission list in 8 days working 7 hours a day. If 3 persons join them so as to complete the work in 4 days, they need to work per day for ?

• (A) 6 hours
• (B) 8 hours
• (C) 10 hours
• (D) 12 hours

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 Let the number of working hours per day be x More persons, Less working hours ( Indirect proportion) Less days, More working hours (Indirect proportion) \[\left. \begin{gathered} {\text{Persons 7}}:4 \hfill \\ {\text{Quantity 4}}:8 \hfill \\ \end{gathered} \right\}::7:x\] $$\eqalign{ & \therefore {\text{ }}7 \times 4 \times x = 4 \times 8 \times 7 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 8 \times 7} \right)}}{{\left( {7 \times 4} \right)}} \cr & \Leftrightarrow x = 8 \cr} $$

66.

12 men and 18 boys, working $$7\frac{1}{2}$$ hours a day, can do a piece of work in 60 days. If a man works equal to 2 boys, then how many boys will be required to help 21 men to do twice the work in 50 days, working 9 hours a day ?

• (A) 30
• (B) 42
• (C) 48
• (D) 90

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 1 man ≡ 2 boys ⇔ (12 men + 18 boys)           ≡ (12 × 2 ×18) boys = 42 boys Let required number of boys = x ⇒ (21 men + x boys) ≡ (21 × 2 × x) boys = (42 + x) boys Less days, More boys (Indirect proportion) More hours per day, Less boys (Indirect proportion) More work, More boys (Direct proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 50}}:60 \hfill \\ {\text{Hours per day 9}}:\frac{{15}}{2} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Work }}1:2 \hfill \\ \end{gathered} \right\}::42:\left( {42 + x} \right)\] $$\therefore \left[ {50 \times 9 \times 1 \times \left( {42 + x} \right)} \right] = $$     $$\left( {60 \times \frac{{15}}{2} \times 2 \times 42} \right)$$ $$\eqalign{ & \Leftrightarrow \left( {42 + x} \right) = \frac{{37800}}{{450}} \cr & \Leftrightarrow 42 + x = 84 \cr & \Leftrightarrow x = 42 \cr} $$