Simple Equations STD VI

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

Answer:

Let Shobo’s present age by y.

So, Shobo’s mother’s present age is 6y.

Also given, (y + 5) = 1/3 x 6y

Or, y + 5 = 2y

Or 2y – y = 5

Or, y = 5

So, Shobo’s age is 5.

And Shobo’s mother’s age is 6y = 30. 

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs100 per meter it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?

Answer:

Let the length of the plot be L

Let the breadth of the plot be B

So, given L:B = 11: 4

Or, 4L = 11B

Or, B = 4L /11

Now perimeter of the rectangular plot is

= 2 ( L + B)

= 2 ( L + 4L/11)  because B = 4L/11

Now given that 100 x 2(L + 4L/11) = 75000

Or, 200(L + 4L /11) = 75000

Or, L (1 + 4/11) = 75000/200

Or, L(15/11) = 375

Or, L = 375 x 11/15 = 25 x 11 = 275

So, the length of the plot is 275 meters

And the breadth of the plot is 4x275/11 = 4 x 25 = 100 meters.

Check:

2(275+100) x 100 = 750x100 = 75000