Find the fraction which becomes 1/2 when its numerator is increased by 6 and is equal to 1/3 when its denominator is increased by 7.

Let the numerator be x and denominator be y. Thus, fraction = Given, The fraction becomes when its numerator is increased by 6. ⇒ ⇒ 2(x + 6) = y ⇒ 2x + 12 = y ..........(1) Given, The fraction becomes when its denominator is increased by 7. ⇒ ⇒ 3x = y + 7 .......(2) Substituting value of y from equation (1) in (2), we get : ⇒ 3x = (2x + 12) + 7 ⇒ 3x = 2x + 19 ⇒ 3x - 2x = 19 ⇒ x = 19. Substituting value of x in equation (1), we get : ⇒ 2 × 19 + 12 = y ⇒ 38 + 12 = y ⇒ y = 50. Hence, the fraction = .

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

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Mathematics

Find the fraction which becomes 1/2 when its numerator is increased by 6 and is equal to 1/3 when its denominator is increased by 7.

Linear Equations

Related Questions

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.

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