Q10 of 168 Page 7

The difference of two numbers is 5 and the difference of their reciprocals is Find the numbers.

Let the first number be ‘X’, so the other number will be ’(X+5)’.

On simplifying further,

X² + 5X – 50 = 0

On applying Sreedhracharya formula

∴ X = –10 or X = 5.

Then other numbers will be (X+5) = {–10+5} & {5+5} i.e., –5 or 10.

∴ The numbers are –10 & –5 or 5 & 10.

A two–digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.

The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

The sum of a number and its reciprocal is . Find the number.

Divide 12 into two parts such that the sum of their squares is 74.