Page 41 - SM inner class 8.cdr

Solution: 9x + 12 =120 - 9x - 54
(i) 10 × 5 + 6 = 50 + 6 = 56 9x + 12 = 66 - 9x
9x + 9x = 66 -12
(ii) 100 × 7 + 10 × 1 + 8 = 718
18x = 54
(iii) 100 × a + 10 × c + b = acb
x = 3
Example 3. In a two digit number, the digit of
Original number =120 - 9x
the unit place is double the digit in the tens
(
place. The number exceeds the sum of its digit =120 - 9 3)
by 18. Find the number. =120 - 27

Solution: Let the digit in the tens place of the Original number = 93
number be x. Example 5. The sum of a two digit number and
The digit in the units place of the number the number obtained by reversing the order of
= 2x (double of ten’s place) the digit is 165. If the tens and unit’s digits are
x
\ The number =10( ) + 2x =12x differ by 3, find the original number.
Sum of the digits = x + x = x Solution: Let unit digit = x
3
2
Given that the number exceeds the sum of its Ten’s digit = x + 3
digit by 18. Original number =10(x + 3) + x
Þ 12x = 3x + 18 =10x + 30 + x
Þ 9x =18 Original number =11x + 30
Þ x = 2
Reversing the digits :
Therefore, the digit in the tens place is 2 and
the digit in the units place is (2 ´ 2) i.e. 4. Unit digit = x + 3
So, the number is 24. Ten’s digit = x
Example 4. The sum of digits of two-digit New number =10x + x + 3
number is 12. If the new number formed by New number =11x + 3
reversing the digits is less than the original As the sum of original number and the new
number by 54 .Find the original number. number =165

Solution: Let the unit digit = x 11x + 30 + 11x + 3 =165
Ten’s digit =12 - x 22x + 33 =165
x
Original number =10 12( - ) + x 22x =132
-
=120 10x + x x = 6
Original number =120 - 9x Original number =11x + 30
=11x + 30 11 6) + 30
(
=
Now, on Reversing the digits :
= 66 + 30
Unit digit =12 - x
= 96
Ten’s digit = x
Here you may get answer as 69 also.
New number =10x + 12 - x
New number = 9x + 12
As new number is less than the original
number by 54

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Mathematics In Focus - 8