Chain Rule Questions Answers

• 1. If 16 toys cost 240, then what do 40 toys cost ?

  1. Rs. 600
  2. Rs. 620
  3. Rs. 640
  4. Rs. 660

  Answer And Explanation

  Answer: Option C

  Explanation:

  Although we can first calculate the cost of one toy and then can multiply it with 40 to get the result.
  but we will solve it with chain rule so that we can prepare ourself for other complex problems which we can solve easily by applying this rule.
  
  Let the required cost be Rs. x
  More toys means More Cost. (Direct Proportion)
  
  \begin{aligned}
  15:40 :: 240:x \\
  => x = \frac{240*40}{15} \\
  => x = 640
  \end{aligned}
  
  So 40 toys will cost Rs 640

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• 2. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate ?

  1. xd
  2. yd
  3. yd/x
  4. x/yd

  Answer And Explanation

  Answer: Option C

  Explanation:

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• 3. If the price of 23 toys is 276, then what will the price of 12 toys ?

  1. 144
  2. 148
  3. 156
  4. 186

  Answer And Explanation

  Answer: Option A

  Explanation:

  Less toys, Less Price (Direct Proportion)
  So, let the price be Rs. x
  then,
  \begin{aligned}
  23:12 :: 276:x
  => x = \frac{276*12}{23} \\
  => x = 144
  \end{aligned}
  
  So price of 12 toys will be Rs. 144

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

  1. 45 paise
  2. 46 paise
  3. 47 paise
  4. 48 paise

  Answer And Explanation

  Answer: Option D

  Explanation:

  Quarter of Kg means 250 gm
  
  Less weight, less price (Direct Proportion)
  So,
  \begin{aligned}
  250:200 :: 60:x \\
  => x = \frac{200*60}{250} \\
  => x = 48
  \end{aligned}
  
  So 200 gm will cost 48 paise.

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• 5. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?

  1. 194 seconds
  2. 195 seconds
  3. 196 seconds
  4. 197 seconds

  Answer And Explanation

  Answer: Option B

  Explanation:

  Let the time required by x seconds.
  Then, More cloth means More time (Direct Proportion)
  So,
  \begin{aligned}
  0.128 : 1 :: 25 : x
  => x = \frac{25*1}{0.128} \\
  => x = 195.31
  \end{aligned}
  
  So time will be approx 195 seconds

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• 6. A flagstaff 17.5 metre high casts a shadow of length 40.25 metre. The height of building, which casts a shadow of length 28.75 metre under similar conditions will be :

  1. 12 metre
  2. 12.5 metre
  3. 13.5 metre
  4. 14 metre

  Answer And Explanation

  Answer: Option B

  Explanation:

  Less shadow, Less Height (Direct Proportion)
  So, let height of building be x metre
  then,
  \begin{aligned}
  40.25 : 17.5 :: 28.75 : x \\
  
  => x = \frac{17.5*28.75}{40.25} \\
  => x = 12.5
  \end{aligned}
  
  So height of building should be 12.5 metre

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• 7. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?

  1. 24 days
  2. 28 days
  3. 34 days
  4. 35 days

  Answer And Explanation

  Answer: Option A

  Explanation:

  Less Men, means more Days {Indirect Proportion}
  
  Let the number of days be x
  then,
  
  27 : 36 :: 18 : x
  [Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
  
  \begin{aligned}
  x = \frac{36*18}{27} \\
  x = 24
  \end{aligned}
  So 24 days will be required to get work done by 27 men.

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