Q5 of 186 Page 4

Two positive numbers differ by 3 and their product is 54. Find the numbers.

Let the two numbers be x and y.

According to the question,

x – y = 3 …(i)

Also, x×y = 54

…(ii)

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

⇒ 54 – y² = 3y

⇒ y² + 3y – 54 = 0

⇒ y² + 9y – 6y – 54 = 0

⇒ y(y + 9) – 6(y + 9) = 0

⇒ (y – 6)(y + 9) = 0

⇒ y = – 9 and 6

But y = – 9 can’t be the one number as it is given that the numbers are positive.

Hence, the two numbers are 9 and 6.

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.

Two numbers are in the ratio of 3 : 5. If 5 is subtracted from each of the number they become in the ratio of 1 : 2. Find the numbers.

Two numbers are in the ratio of 3 : 4. If 8 is added to each number, they become in the ratio of 4 : 5. Find the numbers.