Question

Sum and difference of two numbers are 21 and11 respectively.Find the greater number.​

Answer 1

Answer:

We don't know the numbers, so let's assign variables and write out what each statement means algebraically:

x + y = 21 (the sum of two numbers is 21)

x - y = 11 (the difference of those numbers is 11)

This is a system of linear equations. We have two unknowns and two linearly independent equations, so there's exactly one solution. We can easily find it through elimination, by subtracting the terms of the second equation from the first on each side of the equation:

x + y - (x - y) = 21 - 11

x - x + y + y = 10

2y = 10

y = 5

Now that we have one of the values, we plug its value into either of the original equations to find the other:

x + y = 21

x + 5 = 21

x = 21 - 5

x = 16

And there we have it; the greater number is 16.

Answer 2

Step-by-step explanation:

Let the no.s be x and y

As per first condition,

x+y=21 .............(i)

As per second condition,

x-y=11

x=11+y ...........(ii)

Substituting (ii) in (i),

(11+y)+y=21

2y=10

y=5

Substituting the value of y in (ii)

x=11+5

x=16

Therefore the greater no. is 16

Hope it helps