Question

Divide 87 in three parts such that all parts are in A.P and product of two smaller parts will be 783

Answer 1

Given :-

◉ Number 87 which has to be divided in three parts such that they are in AP and product of two smaller parts will be 783

To Find :-

◉ terms of AP

Solution :-

It is given that 87 has to be divided into three parts which are in AP, Let the parts be

⇒ a - d , a , a + d

Now, the sum of the three parts would be 87 because we are dividing 87 into three parts,

⇒ Sum of three terms = 87

⇒ a - d + a + a + d = 87

⇒ 3a = 87

⇒ a = 29 ...(1)

Further, It is given that the product of two smaller parts will be 783, Here the two parts are a - d and a because a + d is greater than each of them,

⇒ a(a - d) = 783

⇒ 29(29 - d) = 783 [ from (1) ]

⇒ 29 - d = 27

⇒ d = 29 - 27

⇒ d = 2

Now, we have found the value of a and d, Let's find the parts in which 87 was divided,

⇒ a + d , a , a - d

⇒ 29 + 2 , 29 , 29 - 2

⇒ 31 , 29 , 27

Hence, 87 will be divided into 31 , 29 , 27.

Answer 2

AnswEr :-

• Three parts are 27, 29 and 31.

Given :-

• 87 should be divided into three parts such that all parts are in A.P. and product of smaller parts will be 783.

To Find :-

• Terms of the A.P.

SoluTion :-

→ Let three parts be

• a - d , a , a + d

→ Sum of three parts is 87

★ According to question :-

→ a - d + a + a + d = 87

→ 3a = 87

→ a = 87/3

→ a = 29

Here,

Two smaller parts are a - d and a

★ Product of these two parts is 783

→ a (a - d) = 783

→ 29 (29 - d) = 783

→ 29 - d = 783/29

→ 29 - d = 27

→ d = 29 - 27

→ d = 2

Put the value of a and d

• a - d = 29 - 2 = 27

• a = 29

• a + d = 29 + 2 = 31

Hence, three parts in which 87 will be divided into are » 27, 29 and 31.

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