The difference between two numbers is 12 and the difference between their squares is 456. Find the numbers.

Let two numbers be x and y, where x y. Given, Difference between two numbers = 12. ⇒ x - y = 12 .........(1) Given, Difference between their squares = 456 ⇒ x2 - y2 = 456 By identity, ⇒ x2 - y2 = (x + y)(x - y) ⇒ (x + y)(x - y) = 456 Substituting value of x - y from equation (1) in above equation, we get : ⇒ (x + y)(12) = 456 ⇒ (x + y) = ⇒ x + y = 38 ........(2) Adding equations (1) and (2), ⇒ x + y + x - y = 38 + 12 ⇒ 2x = 50 ⇒ x = ⇒ x = 25. Substituting value of x in equation (1), we get : ⇒ x - y = 12 ⇒ 25 - y = 12 ⇒ y = 25 - 12 ⇒ y = 13. Hence, the numbers are 25 and 13.

If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is 4 and the remainder is 2. Find the numbers.

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If 2 is added to each of two given numbers, then their ratio becomes 1 : 2. However, if 4 is subtracted from each of the given numbers, the ratio becomes 5 : 11. Find the numbers.

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Mathematics

The difference between two numbers is 12 and the difference between their squares is 456. Find the numbers.

Linear Equations

Related Questions

If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is 4 and the remainder is 2. Find the numbers.

If 2 is added to each of two given numbers, then their ratio becomes 1 : 2. However, if 4 is subtracted from each of the given numbers, the ratio becomes 5 : 11. Find the numbers.