Practice MCQ Questions and Answer on Chain Rule

61.

A canteen requires 651 bananas for a week. Totally, how many bananas will it require for the months of April, May and June ?

• (A) 8463
• (B) 8547
• (C) 9086
• (D) 9284

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 Total number of days = (30 + 31 + 30) = 91 Let the number of bananas be x More days, More bananas (Direct proportion) $$\eqalign{ & \therefore 7:91::651:x \cr & \Rightarrow 7x = 91 \times 651 \cr & \Rightarrow x = \left( {\frac{{91 \times 651}}{7}} \right) \cr & \Rightarrow x = 8463 \cr} $$

62.

Running at the same constant rate, 6 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce on 30 minutes ?

• (A) 225
• (B) 250
• (C) 300
• (D) 350

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 Let the required number of bottles be x More machines, More bottles produced (Direct proportion) Less time, Less bottles produce (Direct proportion) \[\left. \begin{gathered} {\text{Machines 6}}:15 \hfill \\ \,\,\,\,\,\,{\text{Times 60}}:30 \hfill \\ \end{gathered} \right\}::180:x\] $$\eqalign{ & \therefore {\text{ }}6 \times 60 \times x = 15 \times 30 \times 180 \cr & \Leftrightarrow x = \frac{{\left( {15 \times 30 \times 180} \right)}}{{\left( {6 \times 60} \right)}} \cr & \Leftrightarrow x = 225 \cr} $$

63.

If 5 spiders can catch five files in five minutes, how many files can hundred spiders catch in 100 minutes ?

• (A) 100
• (B) 500
• (C) 1000
• (D) 2000

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 Let the required number of chairs be x. Then, More spiders, More flies (Direct proportion) More time, More flies (Direct proportion) \[\left. \begin{gathered} \,\,\,{\text{Spiders 5}}:100 \hfill \\ {\text{Minutes 5}}:100 \hfill \\ \end{gathered} \right\}::5:x\] $$\eqalign{ & \therefore {\text{ }}5 \times 5 \times x = 100 \times 100 \times 5 \cr & \Leftrightarrow x = \frac{{\left( {100 \times 100 \times 5} \right)}}{{\left( {5 \times 5} \right)}} \cr & \Leftrightarrow x = 2000 \cr} $$

64.

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

• (A) $$29\frac{1}{5}$$
• (B) $$37\frac{1}{4}$$
• (C) 42
• (D) 54

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 After 10 days : 150 men had food for 35 days. Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion) $$\eqalign{ & \therefore 125:150::35:x \cr & \Rightarrow 125 \times x = 150 \times 35 \cr & \Rightarrow x = \frac{{150 \times 35}}{{125}} \cr & \Rightarrow x = 42 \cr} $$

65.

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

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 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

66.

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

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