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प्रश्न
The sum of two numbers is 8. If their sum is four times their difference, find the numbers.
उत्तर
Let the numbers are x and y. One of them must be greater than or equal to the other. Let us assume that x is greater than or equal to y.
The sum of the two numbers is 8. Thus, we have ` x+y =8`
The sum of the two numbers is four times their difference. Thus, we have
` x + y = 4( x -y)`
` ⇒ x + y = 4x - 4y = 0`
`⇒ 4x - 4y - x - y =0`
` ⇒ 3 x -5 y = 0`
So, we have two equations
` x + y = 8`
`3x -5y = 0`
Here x and y are unknowns. We have to solve the above equations for x and y.
Multiplying the first equation by 5 and then adding with the second equation, we have
`5(x + y)+ (3x - 5y)= 5 xx 8 + 0 `
` ⇒ 8 x = 40 `
`⇒ x = 40/8`
`⇒ x = 5`
Substituting the value of x in the first equation, we have
` 5 + y = 8`
`⇒ y = 8 - 5 `
`⇒ y =3`
Hence, the numbers are 5 and 3.
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