Question

Q 30 Three numbers are in A.P. and their sum is 69. Also, the product of first two numbers is 483. Determine the three numbers.
Ops: A.
None of the mentioned options
B.
О 21, 23, 25
C.
O 25, 23, 21
D.
O 19, 22, 25​

Answer 1

Answer:

The numbers are 21, 23, 25

Step-by-step explanation:

Let the numbers be a, (a + d), (a + 2d).

Now, according to the Question,

a + (a + d) + (a + 2d) = 69

a + a + d + a + 2d = 69

3a + 3d = 69

3(a + d) = 69

a + d = 69/3

a + d = 23 ----- 1

Also,

a × (a + d) = 483

a(a + d) = 483

From eq.1 we get,

a(23) = 483

a = 483/23

a = 21

So,

a = 21

a + d = 23

21 + d = 23

d = 23 - 21

d = 2

Hence,

a + 2d = 21 + 2(2)

= 21 + 4 = 25

Hence,

The numbers are 21, 23, 25.

Hope it helped and believing you understood it........All the best

Answer 2

Answer:

21 , 23 and 25 are the required three numbers.

Step-by-step explanation:

Explanation:

Given, three number are in A.P and their sum is  69.

And the product of first two numbers is 483.

Let   the three  numbers be, (a -d), a , (a +d).

Step 1:

According to the question sum of numbers = 69

(a -d) + a+ (a +d) = 69

⇒3a = 69

⇒a = $\frac{69}{3}$ = 23.........(i)

Step 2:

And product of first two numbers = 483

⇒ (a -d) a = 483

⇒$a^2 -ad$ = 483

Now from (i), on putting the value of a = 23 we get,

⇒ $(23)^2$ - (23) d = 483

⇒529 - 23d = 483

⇒529 - 483 = 23d

⇒46 = 23d

⇒d =$\frac{46}{23}$ = 2

So, the numbers are,

a = 23 , (a -d ) = 23 -2 = 21 and (a +d) = 23 +2 = 25.

Final answer:

Hence, the numbers are, 21 , 23 and 25.

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