RPSC RAS (Rajasthan) Exam > RPSC RAS (Rajasthan) Notes > RAS RPSC Prelims Preparation - Notes, Study Material & Tests > 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC
3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) PDF Download
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
- Direct Proportion
Two quantities are said to be directly proportional, if on the increase or decrease of the one, the other increases or decreases the same extent.
Examples
- Cost of the goods is directly proportional to the number of goods. (More goods, More cost)
- Amount of work done is directly proportional to the number of persons who did the work. (More persons, More Work)
- Indirect Proportion (inverse proportion)
Two quantities are said to be indirectly proportional (inversely proportional) if on the increase of the one, the other decreases to the same extent and vice-versa.
Examples
- Number of days needed to complete a work is indirectly proportional (inversely proportional) with the number of persons who does the work (More Persons, Less Days needed)
- The time taken to travel a distance is indirectly proportional (inversely proportional) with the speed in which one is travelling (More Speed, Less Time)
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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FAQs on 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC - RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan)
| 1. What is the chain rule in calculus? |  |
Ans. The chain rule is a fundamental concept in calculus that allows us to find the derivative of a composite function. It states that if we have a function composed of two or more functions, then the derivative of the composite function can be found by multiplying the derivatives of the individual functions and following a specific formula.
| 2. How is the chain rule applied in solving mathematical problems? | |
Ans. The chain rule is applied by first identifying the composite function and breaking it down into its individual functions. Then, we find the derivative of each individual function. Finally, we multiply the derivatives together according to the chain rule formula to obtain the derivative of the composite function.
| 3. What is the importance of the chain rule in real-world applications? | |
Ans. The chain rule is essential in real-world applications involving rates of change. It allows us to analyze complex systems by breaking them down into simpler functions and understanding how changes in one variable affect the overall system. For example, in physics, the chain rule is used to calculate velocities, accelerations, and other derivatives in motion problems.
| 4. Can you provide an example of how to use the chain rule in solving a problem? | |
Ans. Sure! Let's say we have a function f(x) = sin(3x^2 + 2x). To find the derivative of this function, we can apply the chain rule. First, we identify the inner function as g(x) = 3x^2 + 2x and the outer function as h(x) = sin(x). Taking the derivatives, we get g'(x) = 6x + 2 and h'(x) = cos(x). Finally, we apply the chain rule formula: f'(x) = g'(x) * h'(g(x)). Therefore, f'(x) = (6x + 2) * cos(3x^2 + 2x).
| 5. Are there any common mistakes to avoid when using the chain rule? | |
Ans. Yes, there are a few common mistakes to avoid when using the chain rule. One mistake is forgetting to multiply the derivatives of the individual functions together. Another mistake is mixing up the order of the functions when applying the chain rule formula. It's important to correctly identify the inner and outer functions to ensure the correct application of the chain rule. Additionally, being cautious about simplifying expressions too early or incorrectly can also lead to mistakes.
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