Practice MCQ Questions and Answer on Chain Rule

41.

The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozens of such mangoes ?

• (A) Rs. 3000
• (B) Rs. 3500
• (C) Rs. 4000
• (D) Rs. 2500

Show Answer

 Let the required price be Rs. x More mangoes, More price (Direct proportion) $$\eqalign{ & \therefore 357:\left( {49 \times 12} \right)::1517.25:x \cr & \Leftrightarrow 357x = \left( {49 \times 12 \times 1517.25} \right) \cr & \Leftrightarrow x = \frac{{\left( {49 \times 12 \times 1517.25} \right)}}{{357}} \cr & \Leftrightarrow x = 2499 \cr} $$ Hence, the approximate price is Rs. 2500

42.

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

• (A) 648
• (B) 1800
• (C) 2700
• (D) 10800

Show Answer

 Let the required number of bottles be x. More machines, More bottles (Direct Proportion) More minutes, More bottles (Direct Proportion) \[\left. \begin{gathered} {\text{Machines}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{6}}:10 \hfill \\ {\text{Time(in min}}{\text{.)}}\,\,{\text{1}}:4 \hfill \\ \end{gathered} \right\}::270:x\] $$\eqalign{ & \therefore 6 \times 1 \times x = 10 \times 4 \times 270 \cr & \Rightarrow x = \frac{{ {10 \times 4 \times 270} }}{{ 6 }} \cr & \Rightarrow x = 1800 \cr} $$

43.

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

44.

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

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

Show Answer

 Work done = $$\frac{5}{8}$$ Balance work $$ = \left( {1 - \frac{5}{8}} \right)$$   $$ = \frac{3}{8}$$ Less work, Less days ( Direct proportion) Let the required number of days be x Then, $$\eqalign{ & \Leftrightarrow \frac{5}{8}:\frac{3}{8}::10:x \cr & \Leftrightarrow \frac{5}{8} \times x = \frac{3}{8} \times 10 \cr & \Leftrightarrow x = \left( {\frac{3}{8} \times 10 \times \frac{8}{5}} \right) \cr & \Leftrightarrow x = 6 \cr} $$

45.

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) $$\eqalign{ & \therefore {\text{ }}20:14::70:x \cr & \Leftrightarrow \left( {20 \times x} \right) = \left( {14 \times 70} \right) \cr & \Leftrightarrow x = \frac{{\left( {14 \times 70} \right)}}{{20}} \cr & \Leftrightarrow x = 49 \cr} $$

46.

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

Show Answer

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

47.

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

• (A) 1
• (B) $$\frac{7}{2}$$
• (C) 7
• (D) 49

Show Answer

 Let the required number days be x. Less spiders, More days (Indirect Proportion) Less webs, Less days (Direct Proportion) \[\left. \begin{gathered} {\text{Spiders}}\,\,\,\,\,1:7 \hfill \\ \,\,\,{\text{Webs}}\,\,\,\,\,7:1 \hfill \\ \end{gathered} \right\}::7:x\] $$\eqalign{ & \therefore 1 \times 7 \times x = 7 \times 1 \times 7 \cr & \Rightarrow x = 7 \cr} $$

48.

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

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

49.

5 persons can prepare an admission list in 8 days working 7 hours a day. If 2 persons join them so as to complete the work in 4 days, they need to work per day for ?

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

Show Answer

 Let the number of working hours per day be x More persons, Less working hours ( Indirect proportion) Less days, More working hours (Indirect proportion) \[\left. \begin{gathered} {\text{Persons 7}}:5 \hfill \\ {\text{Quantity 4}}:8 \hfill \\ \end{gathered} \right\}::7:x\] $$\eqalign{ & \therefore {\text{ }}7 \times 4 \times x = 5 \times 8 \times 7 \cr & \Leftrightarrow x = \frac{{\left( {5 \times 8 \times 7} \right)}}{{\left( {7 \times 4} \right)}} \cr & \Leftrightarrow x = 10 \cr} $$

50.

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) \[\left. \begin{gathered} {\text{Gardeners & grass mowers 8}}:4 \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Area 400}}:800 \hfill \\ \end{gathered} \right\}::4:x\] $$\eqalign{ & \therefore {\text{ }}8 \times 400 \times x = 4 \times 800 \times 4 \cr & \Leftrightarrow x = \frac{{\left( {4 \times 800 \times 4} \right)}}{{\left( {8 \times 400} \right)}} \cr & \Leftrightarrow x = 4 \cr} $$