# Chain Rule Formulas for Competitive Exams

Chain Rule is a mathematical, topic. This topic is easier than other topics. If you practice this topic from the formulas, then you can easily solve the questions in this topic. Here are some questions in the blog that have been solved with the help of formula.

Therefore you should practice chain rule questions with chain rule formula for better results in banking and SSC exams. Students should prepare for exams by practicing **chain rule questions** with their answers.

**Important Chain Rule Formulas**

**1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increase (or decrease) to the same extent.**

**Ex.1. **cost is directly proportional to the number of men working on it.

(More Articles, More Cost)

**Ex.2. **Work done is directly proportional to the number of men working on it.

(More Men, More Work)

**2. Indirect Proportion: Two quantities are said to be indirectly proportional if on the increase of the one, the other decreases to the same extent and vice-versa.**

**Ex.1. **The time taken by a car in covering a certain distance is inversely proportional to the speed of the car.

(More speed, Less is the time taken to finish a job)

**Ex.2. **Time taken to finish a work is inversely proportional to the number of persons working at it.

(More person, Less is the time taken to finish a job)

**Remark: In solving the question by chain rule, we compare every item with the term to be found out.**

**Ex.1. If 15 toys cost Rs. 234, what do 35 cost?**

**Solution**

Let the required cost be Rs. x. Then,

More toys, More cost (Direct Proportion)

$$⸫ 15 : 35 : : 234 : x ⟺ (15×x)=(35×234)⟺x={35×234\over 15}=546.$$

Hence, the cost of 35 toys is Rs. 546

**Ex.2. If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?**

**Solution**

Let the required number of hours be x. Then,

Less men, More hours (Indirect Proportion)

$$∴ 15 : 36 :: 25 : x ⟺ (15×x)=(36×25)⟺ x={36×25\over 15}=60 $$

Hence, 15 men can do it in 60 hours.

**Ex.3. If the wages of 6 men for 15 days-be Rs. 2100, then find the wages of 9 men for 12 days.**

**Solution**

Let the required wages be Rs. x.

More men, More wages (Direct Proportion)

Less days, Less wages (Direct Proportion)

$$ \left(Men \ 6:9, Days \ 15 : 12\right):: 1200 : x $$

$$∴ (6×15×x)=(9×12×2100)⟺ x={9×12×2100\over 6×15}=2520 $$

Hence, the required wages are Rs. 2520.

**Ex.4. If 20 men can build a wall 56 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days?**

**Solution**

Let the required length be x meters.

More men, More length built (Direct Proportion)

Less days, Less length built ( Direct Proportion)

$$ \left(Men \ 20 : 35, Days \ 6 : 3\right) :: 56 : x$$

$$ ∴ (20×6×x)=(35×3×56)⟺ x = {(35×3×56)\over 120}=49 $$

Hence the required length is 49 m.

**Ex.5. If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working reap the filed working 8 hours a day?**

**Solution**

Let the required number of days be x.

More men, Less days (Indirect Proportion)

Less hours per day, More days (Indirect Proportion)

$$ \left(Men \ 18 : 15, Hours \ Per \ Days \ 8 : 9\right) :: 16 : x$$

$$ ∴ (18×8×x)=(15×9×16)⟺ x = {(15×144)\over 144}=15 $$

Hence the required number of days = 15.