Question

the sum and difference of two num are 27and11 respectively then the num are​

Answer 1

Solution :

Let the numbers be x and y. [ x > y ( say ) ]

Sum of numbers = x + y

Difference of numbers = x - y

According to question :

Sum of numbers = 27

=> x + y = 27 _____(1)

Difference of numbers = 11

=> x - y = 11 _______(2)

Solving equations (1) and (2) :

x + y = 27

=> x = 27 - y

put x = 27 - y in equation (2)

(27-y) - y = 11

=> 27 - y - y = 11

=> 27 - 2y = 11

=> -2y = 11 - 27

=> -2y = -16

=> y = $\cancel\dfrac{-16}{-2}$

=> y = 8

Now put y = 8 in equation (1)

x + y = 27

=> x + 8 = 27

=> x = 27 - 8

=> x = 19

Verification :

put x = 19 and y = 8 in equation (1)

=> 19 + 8 = 27

=> 27 = 27

Hence, x = 19 and y = 8 ( correct answer )

Answer 2

$\huge{\text{\underline{Solution:-}}}$

★ Given:-

• Let the numbers be x and y [ where, x > y]
• Sum of numbers = x + y
• Difference of numbers = x - y

★ According to question:-

Sum of numbers = 27

=> x + y = 27 _____(1)

Difference of numbers = 11

=> x - y = 11 _______(2)

Solving equations (1) and (2)

x + y = 27

=> x = 27 - y

Put x = 27 - y in equation (2)

(27-y) - y = 11

=> 27 - y - y = 11

=> 27 - 2y = 11

=> -2y = 11 - 27

=> -2y = -16

=> y = $\cancel\dfrac{-16}{-2}$

=> y = 8

Now put y = 8 in equation (1)

x + y = 27

=> x + 8 = 27

=> x = 27 - 8

=> x = 19

★ Verification:-

Put x = 19 and y = 8 in equation (1)

=> 19 + 8 = 27

=> 27 = 27

Hence, x = 19 and y = 8

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