Question

EXERCISE- 5.1
its interchange the
itself. Find the
63. What is the de
s digits are rever
1. A number consists of two digits whose sum is 9. If 9 is subtracted from the number, the digits interchan
Find the number.
2. The units digit of a two digit number is 2 and itself. Fin
3. The difference between a 2-digit number and the number obtained by interchanging its digits is 63. What i
between the digits of the number?
4. A two digit number is 6 more than 4 times the sum of its digits. If 27 is added to the number, its digits arer
the number.
3. A number consists of two digits of which ones digit exceeds the tens digit by 1. The number itself is equal
the sum of its digits. Find the number.
6. The ratio of the digits of a three digit number is 1:2:3. On adding 396 to the number, the digits are reversed
number.
7. A certain number between 10 to 100 is 8 times the sum of its digits and if 45 is subtracted from it, the digit
reversed. Find the number.
8. In a 3-digit number, the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Ift
the digits is 16, find the number.
9. A two digit number is 5 times the sum of its digits. If9 is added to the number, its digits are reversed. Find the nu
10. A number consists of three digits, the right hand digit being zero. If the left hand and the middle digits be inte
the number is diminished by 180. If the left hand digit be halved and the middle and right hand digits be interch
number is diminished by 454. Find the number.
TESTS OF DIVISIBILITY
Tests
Rules
Examples​

Answer 1

Answer:

54

Step-by-step explanation:

1 ; Let say number = XY

Value = 10X + Y

X + Y = 9  

Value = 10X + (9-X) = 9X + 9

9 is subtracted from the number, the digits interchange

=> 9X + 9 - 9 = 9X

9X = 10Y + X

=> 8X = 10Y

=> 4X = 5Y

=>4X =5(9-X)

=> 4X = 45 - 5X

=> 9X = 45

=> X = 5

& Y = 4

Number = 54

3.   XY Value 10X + Y

   YX Value = 10Y + X

10X + Y - (10Y + X)  = 63

=> 9(X - Y) = 63

=> X - Y = 7

Difference between the digits of the numbers = 7

4 .

10X + Y  = 6 + 4(X + Y)

=> 10X + Y = 6 + 4X + 4Y

=> 6X - 3Y = 6

=> 2X - Y = 2

10X + Y + 27 = 10Y + X

=> 9Y - 9X = 27

=> Y - X  = 3

X = 5

Y = 8

Number = 58