More Interesting question

A figure is made up of a square and a rectangle overlapped each other as shown below. The ratio of the area of the square to the ratio of the are of the rectangle is 3:2. The shaded area of the rectangle is 3/8 of the area of the rectangle. The total unshaded area is 42cm² . What is the area of the rectangle?

It is relative common for MOE to set a typical question like this. Firstly ratio is provided between the area of the square & area of the rectangle. Then the fraction of shaded area of the rectangle is provided. Finally, the area of the unshaded is provided so that you can determine the area of rectangle.

In order to compare the item properly, we can compare the items in units as below :-

Since the shaded area of the rectangle is 3/8. We can represent the shaded portion of the rectangle as 3 units and the unshaded portion as 5 units. As the area of the rectangle take up 2 parts, which is 8 units in total, we can simply said that 1 parts is equal to 4 units. Since the rectangle is 2 parts then the square is 3 parts, which will take up 12 units. The interlapped took up 3 units, hence the unshaded portion of the square will be 9 units (12units - 3 units). The unshaded portion make up by unshaded rectangle portion (5 units) and the unshaded square portion ( 9 units), so the total unshaded area is 14 units.

14 units     42cm²

1 units       42/ 14 = 3cm²

         

Since the area of rectangle is made up of 8 units

8 units      3cm² X 8 = 24cm²

Word Problem - Ratio

Question   :

A farmer has equal number of chickens and ducks. After he sold 10 chickens and 36 ducks, The ratio of chickens he has to the ratio of duck he has became 3:1. How many chickens do he had at first?

Model Methods

Different remaining = Difference sold

               

                 2 units         26

                 1 unit  13

At first the farmer had 3 x 13 + 10 = 49 chickens

Alternate Methods

Make sure both the final quantities (3 parts and 1 part) are equal. Multiply the entire column by the same number

then we have the following table

As both the chickens and ducks are having the same final quantities, we can find out the below

2 units108 - 10   =   98

1 unit  49

                                                                                                             ANS :       49 chickens