### 1. Direct Proportion**:**

Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

E.g. Cost is directly proportional to the number of articles. (More Articles, More Cost)

### 2**. **Indirect Proportion:

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

E.g. The time taken by car is covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time to cover a distance.)

Note: In solving problems by chain rule, we compare every item with the term to be found out:

Solved Illustrations:

### Question 1)

If the cost of X meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?

A) Rs. xy/d

B) Rs. yd/x

C) Rs. (yd)

D) Rs. (xd)

Answer: option **B**

Solution:

Cost of x metres = Rs. d.

Cost of 1 metre = Rs. d/x

Cost of Y metres = Rs. (d/x * x.y) = rs. yd/x

### Question 2)

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) 10

B) 13

C) 14

D) 15

Answer: Option **B**

Solution

Let the required number of days be X.

Less person, more days (indirect proportion)

More working hours per day, Less days (indirect proportion)

Persons 30: 39

Working hours/days 6:5

Therefore, 30*6*x = 39*5*12

X = (39*5*12)

X= 13.

### Question 3)

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

A) 48 paise

B) 54 paise

C) 56 paise

D) 72 paise

Answer: option **A**

Solution: Let the required weight be x kg

Less weight, less cost (direct Proportion)

Therefore, 250:200::60:x = 250 x x = (200*60)

X = (200*60)/250

X = 48

### Question 4)

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

A) 1

B) 1/10

C) 40

D) 80

Answer: Option **C**

Solution:

Let the required number of days be x.

Less cows, more days (Indirect Proportion)

Less bags, Less days (Direct Proportion)

Cow 1:40

Bags 40:1

1*40*x =40*1*40

= x=40.

### Question 5)

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

A) 10.0 m

B) 12.5 m

C) 17.5 m

D) 21.25 m

Answer: option **B**

Solution:

Let the height of the building x metres.

Less lengthy shadow, Less in the height (Direct Proportion)

40.25: 28.75: 17.5: X

40.25 * X = 28.75 * 17.5

X = 28.75*17.5/ 40.25

X = 12.5

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