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Which of the following statements are correct ? A. The sum of three consecutive multiples of 3 is 72. The largest number is 27. B. A number when multiplied by 13 is increased by 180. The number is 13. C. The average of first 20 multiples of 7 is 73.5. Choose the correct answer from the options given below:

Which of the following statements are correct ? A. The sum of three consecutive multiples of 3 is 72. The largest number is 27. B. A number when multiplied by 13 is increased by 180. The number is 13. C. The average of first 20 multiples of 7 is 73.5. Choose the correct answer from the options given below: Correct Answer <span style="">A and C only</span>

Given:

A. The sum of three consecutive multiples of 3 is 72. The largest number is 27.

B. A number when multiplied by 13 is increased by 180. The number is 13.

C. The average of first 20 multiples of 7 is 73.5.

Formula used:

Average = ( First term + Last term ) / 2

Calculation: 

Let the sum of three consecutive multiple of 3 is

( 3n ) + ( 3n + 3 ) + ( 3n + 6 ) = 72_____(i)

Largest no. = 27

( 3n + 6 ) = 27

3n = 27 - 6 = 21

n = 7

Put n=7 in (i)

( 3 ×7 ) + ( 3 × 7 + 3 ) + ( 3 × 7 + 6 ) = 21 + 24 + 27 = 72 (True)

Largest no. = 3 × 7 + 6 = 21 + 6 = 27 (True)

Now, the statement1 is true. 

Statement2 says that a number when multiplied by 13 is increased by 180. The number is 13.

Let the no. = x

According To Question, 

( 13 × x )= x + 180

13x - x = 180

12x = 180

x = 15

Now, the number is15.

But statement say the number is 13.

Now, the statement2 is wrong.

Statemen3 says that the average of first 20 multiples of 7 is 73.5.

The first 20 multiple of 7 is 7 + 14 + 21 + .......... 20terms

Here we find 20th term of multiple of 7

We know nth term of A.P is Tn = T1 + (n-1) × d

Tn is nth term of AP

n is no. of terms 

d is common difference

Here, T1 = 7, d = 7, n = 20

T20 = 7 + ( 20 - 1 ) × 7

⇒7+19*7

⇒140

T20 = 140

Average = ( First term + Last term ) / 2

⇒( 7 + 140 ) / 2 = 73.5

Hence,Option3 is correct.

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