Q2 of 186 Page 4

The sum of two numbers is 15 and sum of their reciprocals is . Find the numbers.

Let the two numbers be x and y.

According to the question,

x + y = 15 …(i)

…(ii)

Eq. (ii) can be re - written as

…(iii)

On putting the value of in Eq. (iii), we get

⇒ xy = 50

On putting the value of in Eq. (i), we get

⇒ 50 + y² = 15y

⇒ y² – 15y + 50 = 0

⇒ y² – 10y – 5y + 50 = 0

⇒ y(y – 10) – 5(y – 10) = 0

⇒ (y – 5)(y – 10) = 0

Hence, the two numbers are 5 and 10.

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

The sum of the two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

Two numbers are in the ratio of 5 : 6. If 8 is subtracted from each of the numb, they become in the ratio of 4 : 5. Find the numbers.

The sum of two numbers is 16 and the sum of their reciprocals is 1/3. Find the numbers.