Question

Q. 2. Divide 56 in four parts in A.P. such that the ratio
of the product of their extremes (1st and 4th) to the
product of middle (2nd and 3rd) is 5:6.​

Answer 1

Answer:

Given:

↬ 56 is divided into four parts which form an A.P.

↬ Ratio of the product of extremes of given A.P. to the product of their means is 5:6

To Find:

All the parts of 56

Things to know before solving question

(a+b)(a-b)= a² -b²

Solution:

Let the four parts be a-3d, a-d, a+d, a+3d such that they are in A.P.

Now,

Sum of all parts= 56

⇒ a-3d+a-d+a+d+a+3d= 56

⇒ 4a= 56

⇒ a= 14

Now,

On putting value of a in above equation, we get

Now,

Case-1 ,when d=2

First part= a-3d= 14-3(2)= 8

Second part= a-d= 14-2= 12

Third part= a+d= 14+2= 16

Fourth part= a+3d= 14+3(2)= 20

Case-2 ,when d= -2

First part= a-3d= 14-3(-2)= 20

Second part= a-d= 14-(-2)= 16

Third part= a+d= 14+(-2)= 12

Fourth part= a+3d= 14+3(-2)= 8

Hence, all four parts are 8, 12, 16 and 20.