Question

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Answer 1

Question: The sum of two numbers is 1000 and the difference between their squares is 25600. Find the numbers

Answer:

Numbers are 512.8 and 487.2

Step-by-step explanation: Let the required numbers are x and y.

Given,sum of no. = 1000    

     ⇒ x + y = 1000          ...(1)

Given, diff. of their squares = 25600

    ⇒ x² - y² = 25600

    ⇒ (x + y)(x - y) = 25600

    ⇒ (1000)(x - y) = 25600

    ⇒ x - y = 25600/1000

    ⇒ x - y = 25.6         ...(2)

Adding (1) and (2), we get

x + y = 1000

x - y = 25.6

2x    = 1025.6     ⇒ x = 1025.6/2 = 512.8

Hence,  substitute x in (1),

   ⇒ 512.8 + y = 1000

   ⇒ y = 487.2