Chain Rule Problems and Solutions

• 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 :

  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

• 2. 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 :

  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

• 3. 10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?

  1. 4 hours a day
  2. 5 hours a day
  3. 6 hours a day
  4. 7 hours a day

  Answer :

  Option C

  Explanation:

  
  More Men, Less Hours {Indirect Proportion}
  Less Days, More Hours {Indirect Proportion}
  \begin{aligned}
  \begin{bmatrix}Men & 15 & 10 \\Days & 12 & 18 \end{bmatrix} :: 6 : x \\
  => x * 15 * 12 = 10 * 18 * 6 \\
  => x = \frac{10*18*6}{15*12} \\
  => x = 6
  \end{aligned}

• 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 :

  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.

• 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 :

  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

• 6. 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 the remaining meal ?

  1. 38 men
  2. 32 men
  3. 34 men
  4. 30 men

  Answer :

  Option D

  Explanation:

  There is meal for 200 children. 150 children have taken the meal.
  Remaining meal is to be catered to 50 children.
  Now, 200 children = 120 men
  
  So, 50 Children = 120/200 * 50 = 30 men

• 7. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk ?

  1. 34 days
  2. 40 days
  3. 46 days
  4. 50 days

  Answer :

  Option B

  Explanation:

  Less Cows, More days (Indirect Proportion)
  Less bags, Less days (Direct Proportion)
  
  \begin{aligned}
  \begin{bmatrix}Cows & 1 & 40 \\Bags & 40 & 1 \end{bmatrix} :: 40 : x \\
  => x * 40 * 1= 40 * 1 * 40 \\
  => x = 40
  \end{aligned}