This module will teach you the basics of direct and indirect proportions. These concepts will further help you in time and work questions.
Important Formulas – chain rule
Examples
Solved Examples
1. 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?  
A. Rs. (xd/y)  B. Rs. x/d 
C. Rs. (yd/x)  D. Rs. y/d 
Answer : Option C
Explanation :
cost of x metres of wire = Rs. d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y×d/x)=Rs. (yd/x)
2. 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 remaining meal?  
A. 50  B. 30 
C. 40  D. 10 
Answer : Option B
Explanation :
Meal for 200 children = Meal for 120 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men
Total mean available = Meal for 120 men
Renaming meal = Meal for 120 men  Meal for 90 men = Meal for 30 men
3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?  
A. 26  B. 22 
C. 12  D. 24 
Answer : Option D
Explanation :
Let the required number of days be x
More men, less days (indirect proportion)
Hence we can write as
Men36:27}::x:18 ⇒36×18=27×x ⇒12×18=9×x
⇒12×2=x
⇒x=24
 
A. 15  B. 12 
C. 21  D. 9 
Answer : Option D
Explanation :
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
Cogs 6:14}: x: 21 ⇒6×21=14×x ⇒6×3=2×x ⇒3×3=x ⇒x=9
5. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?  
A. 10  B. 12 
C. 8  D. 15 
Answer : Option B
Explanation :
Let the required hours needed be x
More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)
Hence we can write as
⇒3×2×8=4×1×x
⇒3×2×2=x
⇒x=12
6. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?  
A. 9  B. 12 
C. 10  D. 13 
Answer : Option D
Explanation :
Let the required number of days be x
More hours, less days (indirect proportion)
Hence we can write as
⇒39×5×12=30×6×x ⇒39×5×2=30×x ⇒39=3×x ⇒x=13
7. A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?  
A. 205  B. 200 
C. 180  D. 195 
Answer : Option D
Explanation :
Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
Cloth 0.128:25} :: 1:x
⇒0.128x=25 ⇒x=25/0.128 ⇒25000/128=3125/16≈195
8. 21 goats eat as much as 15 cows. How many goats each as much as 35 cows?  
A. 49  B. 32 
C. 36  D. 41 
Answer : Option A
Explanation :
15 cows ≡ 21 goats
1 cow ≡21/15 goats
35 cows ≡ (21×35)/15 goats≡(21×7)/3 goats≡7×7 goats ≡ 49 goats
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