A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs Class 8

A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs Class 8

Question 1.

A farm has some horses and hens. The total number of heads of these animals is 55 and the total number of legs is 150. How many horses and how many hens are on the farm? Class 8

Can you solve this without letter- numbers?

[Hint : If all the 55 animals were hens, then how many legs would there be? Using the difference between this number and 150, can you find the number of horses?]

Solution:

If total number of hens be 55, then number of legs = 2 × 55 = 110.

So, difference of legs = 150 - 110 = 40.

So, number of horses = [latex]\frac{40}{2}[/latex] = 20

and number of hens = 55 - 20 = 35.

Question 2.

A mother is 5 times her daughter’s age. In 6 years time, the mother will be 3 times her daughter’s age. How old is the daughter now? Class 8

Solution:

Let daughter’s present age is x years.

So, her mother’s present age is 5x years.

After 6 years, their ages be x + 6 and 5x + 6 years.

Thus, 5x + 6 = 3(x + 6).

or 5x + 6 = 3x + 18

or 5x - 3x = 18 - 6

or 2x = 12, i.e., x = [latex]\frac{12}{2}[/latex] = 6.

So, daughter’s present age is 6 years.