Practice MCQ Questions and Answer on Chain Rule

51.

If 7 maids with 7 mops cleaned 7 floors in 7 hours, how long would it take 3 maids to mop 3 floors with 3 mops ?

• (A) $$\frac{7}{3}\text{ hours}$$
• (B) $$\text{3 hours}$$
• (C) $$\frac{49}{3}\text{ hours}$$
• (D) $$\text{7 hours}$$

Show Answer

 Since each maid would work with one mop, So,we shall consider 1 maid and 1 mop as 1 unit Let the required time be x hours Less maids and mops, More time (Indirect proportion) Less floor, Less time (Direct proportion) \[\left. \begin{gathered} {\text{Maids & Mops 3}}:7 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Floors 7}}:3 \hfill \\ \end{gathered} \right\}::7:x\] $$\eqalign{ & \therefore {\text{ }}3 \times 7 \times x = 7 \times 3 \times 7 \cr & \Leftrightarrow x = \frac{{\left( {7 \times 3 \times 7} \right)}}{{\left( {3 \times 7} \right)}} \cr & \Leftrightarrow x = 7 \cr} $$

52.

If 17 labourers can dig a ditch 26 m long in 18 days, working 8 hours a day; how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, each labourer working 9 hours a day ?

• (A) 34
• (B) 51
• (C) 68
• (D) 85

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 Let the total number of men to be engaged be $$x$$ More length, More labourers (Direct proportion) Less days, More labourers (Indirect proportion) \[\left. \begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,{\text{Lentgh 26}}:39 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Days 6}}:18 \hfill \\ {\text{Hours per day }}9:8 \hfill \\ \end{gathered} \right\}::17:x\] $$\eqalign{ & \therefore {\text{ }}26 \times 6 \times 9 \times x = 39 \times 18 \times 8 \times 17 \cr & \Leftrightarrow x = \frac{{\left( {39 \times 18 \times 8 \times 17} \right)}}{{\left( {26 \times 6 \times 9} \right)}} \cr & \Leftrightarrow x = 68 \cr} $$ ∴ Number of more labourers = (68 -17) = 51

53.

If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

• (A) 48 paise
• (B) 54 paise
• (C) 56 paise
• (D) 72 paise

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 $$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{weight}}\,{\text{be}}\,x\,{\text{kg}}. \cr & {\text{Less}}\,{\text{weight,}}\,{\text{less}}\,{\text{cost}}\,\left( {{\text{Direct}}\,{\text{Proportion}}} \right) \cr & \therefore 250:200::60:x \cr & \Rightarrow 250 \times x = {200 \times 60} \cr & \Rightarrow x = \frac{{ {200 \times 60} }}{{250}} \cr & \Rightarrow x = 48 \cr} $$

54.

A flagstaff 17.5 m high caste a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be ?

• (A) 10 m
• (B) 12.5 m
• (C) 17.5 m
• (D) 21.25 m

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 Let the height of the building be x metres Lees lengthy shadow, Less is the height (Direct proportion) $$\eqalign{ & \therefore 40.25:28.75::17.5:x \cr & \Leftrightarrow 40.25 \times x = 28.75 \times 17.5 \cr & \Leftrightarrow x = \frac{{\left( {28.75 \times 17.5} \right)}}{{40.25}} \cr & \Leftrightarrow x = 12.5 \cr} $$

55.

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

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

56.

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) $$7\frac{1}{2}$$

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

57.

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

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

58.

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) \[\left. \begin{gathered} {\text{Pumps 4}}:3 \hfill \\ {\text{Days}}\,\,\,\,\,\,\,\,{\text{1}}:2 \hfill \\ \end{gathered} \right\}::8:x\] $$\eqalign{ & \therefore 4 \times 1 \times x = 3 \times 2 \times 8 \cr & \Rightarrow x = \frac{{ {3 \times 2 \times 8} }}{{ 4 }} \cr & \Rightarrow x = 12 \cr} $$

59.

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

• (A) 4
• (B) 8
• (C) 12
• (D) 16

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 Let the required number of bottles be x. More weavers, More mats (Direct Proportion) More days, More mats (Direct Proportion) \[\left. \begin{gathered} {\text{Wavers}}\,\,\,\,4:8 \hfill \\ \,\,\,\,\,\,{\text{Days}}\,\,\,\,4:8 \hfill \\ \end{gathered} \right\}::4:x\] $$\eqalign{ & \therefore 4 \times 4 \times x = 8 \times 8 \times 4 \cr & \Rightarrow x = \frac{{ {8 \times 8 \times 4} }}{{4 \times 4}} \cr & \Rightarrow x = 16 \cr} $$

60.

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

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