If three numbers are added in pairs, the sums equal to 11,16 and 23.Find the three numbers

a)
8,6,16

b)
9,2,14

c)
9,5,14

d)
7,2,8

Correct answer is option 'B'. Can you explain this answer?

Question

If three numbers are added in pairs, the sums equal to 11,16 and 23.Find the three numbersa)8,6,16b)9,2,14c)9,5,14d)7,2,8Correct answer is option 'B'. Can you explain this answer?

Answer

X+y = 11 - (1)

Y+z = 16 - (2)

Z+x = 23 -(3)

Add (1), (2), and (3)

2(x + y + z) = 50

X+y+z = 25

X = 25 – 16 = 9

y = 25 – 23 = 2

z = 25 – 11 = 14

Answer

X+y = 11
Y+z = 16
Z+x = 23
X+y+z = 25
X = 25 – 16 = 9
y = 25 – 23 = 2
z = 25 – 11 = 14

Answer

X+y = 11
Y+z = 16
Z+x = 23
X+y+z = 25
X = 25 – 16 = 9
y = 25 – 23 = 2
z = 25 – 11 = 14

Answer

Solution:

To solve this question, we can use trial and error method.

Let's assume the three numbers be x, y and z.

Now, we are given that:

x + y = 11 ...(i)

y + z = 16 ...(ii)

x + z = 23 ...(iii)

Adding equations (i), (ii) and (iii), we get:

2x + 2y + 2z = 50

x + y + z = 25

We can now use substitution method to find the values of x, y and z.

From equation (i), we have:

x = 11 - y

Substituting this value in equation (iii), we get:

(11 - y) + z = 23

z = 12 + y

Substituting the values of x and z in equation (ii), we get:

(11 - y) + (12 + y) = 16

y = 3

Substituting the value of y in equations (i) and (ii), we get:

x = 8 and z = 13

Therefore, the three numbers are 8, 3 and 13.

Out of the given options, only option (b) satisfies the given conditions.

Hence, the correct answer is option (b) - 9, 2 and 14.

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