S.chand Class 8 Maths Solution Chapter 22 Playiing With Numbers Exercise 22 A

  Exercise 22 A

Question 1

1. The sum of the digits of a two-digit number is 9 . The number is 6 times the units digit. Find the number.

2. The sum of the digits of a two-digit number is 7 . If the digits are reversed, the new number increased by 3 equals 4 times the original number. Find the original number.

3. The sum of a number of two digits and of the number formed by reversing the digits is 110 , and the difference of the digits is 6 . Find the number.

4. A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the digits will be reversed. Find the number.

5. A number consists of three digits, the right hand being zero. If the left hand and the middle digits be interchanged the number is diminished by 180 . If the left-hand digit be halved and the middle and right-hand digits be interchanged the number is diminished by 454 . Find the number.

[Hint. Let the original number be $100 a+10 b+0$, i.e., $100 a+10 b$, then, by the first condition $(100 a+10 b)-(100 b+10 a)=180 \Rightarrow a-b=2$

By the second condition, new number $=100 \times \frac{a}{2}+0+b=50 a+b$

and so $(100 a+10 b)-(50 a+b)=454 \Rightarrow 50 a+9 b=454]$.