Q4 of 71 Page 62

The sum of the digits of two–digit number is 3. The number obtained by interchanging the digits is 9 less than the original number. Find the original number.

Let the digit at 10s place y and digit at one’s place be x.

∴ 10y + x = The number


Now if we interchange the digits we get a number that is 9 less than the original number.


interchanged number = 10x + y


⇒ 10x + y = 10y + x – 9


⇒ 9x – 9y + 9 = 0


⇒ x – y + 1 = 0 …[1]


and the sum of digits is 3


⇒ x + y = 3 eq[2]


adding eq[1] and …[2]


2x = 2


⇒ x = 1


From eq[1]


x – y + 1 = 0


⇒ y = 2


∴ the original number is 21


More from this chapter

All 71 →
2

The sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.

 3

There are some 25 paise coins and some 50 paise coins in a bag. The total number of coins is 140 and the amount in the bag is Rs. 50. Find the number of coins of each value in the bag.

 5

The length of a rectangle is twice its breadth. The perimeter of the rectangle is 120 cm. Find the length and breadth of this rectangle. Also find its area.

 6

An employee deposits certain amount at the rate of 8% per annum and a certain amount at the rate of 6% per annum at simple interest. He earns Rs. 500 as annual interest. If he interchanges the amount at the same rates, he earns Rs. 50 more. Find the amounts deposited by him at different rates.