Question

Question 3
Let A, B and C be three positive integers such that the sum of A and the
mean of B and C is 5. In addition, the sum of B and the mean of A and C is
7. Then the sum of A and B is
1 4
2) 5
3) 7
4) 6

Answer 1

Step-by-step explanation:

➤ Given :

• Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is.

━━━━━━━━━━━━

➤ To Find :

• The sum of A and B is

━━━━━━━━━━━━

➤ Solution :

$\pink{\fbox{According to the question,}}$

$\implies$A + (B + C)/2 = 5

$\implies$ 2A + B + C = 10 ....(i)

$\implies$ B + (A + C)/2 = 7

$\implies$ 2B + A + C = 14 ....(ii)

➨ Adding both equation we get

$\implies$ 3(A + B) + 2C = 24 ....(iii)

➨ Now we will subtract equation (ii) from equation (i).

$\implies$ B - A = 4 ....(iv)

➨ From option 2 it is not possible that A + B = 4, So option 2 is wrong.

➨ From equation third value of C should be multiple of 3.

Let C = 3 we will put it in equation (iii)

$\implies$3(A + B) + 6 = 24

$\implies$A + B = 18/3

Therefore, the sum of A & B is 6.

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➤ Final Answer :

Therefore, the sum of A & B is 6..

Answer 2

Given:

Three positive integers A, B and C. Sum of A and the mean of B and C is 5. Also, the sum of B and the mean of A and C is 7.

To find:

Sum of A and B i.e. A+B.

Solution:

According to question, we have

$A + \frac{B \: + \:C }{2} = 5$

So,

$2A + B + C = 10 \: \: \: \: (i)$

and

$B + \frac{A + C}{2} = 7$

So,

$2B + A + C = 14 \: \: \: (ii)$

After adding equations (i) and (ii), we get

$3(A + B) + 2C = 24 \: \: \: (iii)$

from equation (iii), it is clear that for the equation to be satisfied, C should be a multiple of 3.

So, after putting C=3 in equation (iii), we have

$A + B = 6$

Hence, the sum of A and B is 6.

So, the correct option is- 4) 6.