Page 65 - SM inner class 8.cdr

According to the question, Therefore, the present age of Jacob is 15 years
(x + 7 ) 3 and the present age of his father = 3x
=
(x + 3 ) -1 2 = 3 × 15 = 45 years.
(x + 7 ) 3 Check: After 5 years,
=
(x + 2 ) 2 Age of Jacob = 15 + 5 = 20 years

2(x + 7) = 3(x + 2) After 5 years,
2x + 14 = 3x + 6 Age of his father = 45 + 5 =50 years
3x - 2x = 14 - 6 Difference of their ages = 50 - 20 = 30 years
x = 8 Example 10: The length of a rectangle is 3 cm
x 8 8 more than its breadth. If its perimeter is 34 cm
The original number i.e., = = .
8
x ( + 3 ) ( + 3 ) 11 find its length and breadth.
Solution: Let the breadth of rectangle be x cm.
Example 8: There are 650 students in a school.
If the number of girls is 106 more than the Therefore, its length = x + 3
boys, how many boys are there in the school? Now, since perimeter = 34 cm
Solution : Let the number of boys = x We have 2(x + 3 + x) = 34

Then, number of girls = x + 106 or 2x + 6 + 2x = 34
x + (x + 106) = 650 (Given in the or 4x = 34 - 6
question)
or 4x = 28 or x = 7
Or 2x + 106 = 650
Therefore, breadth = 7 cm, and length = 7 + 3 =
Or 2x = 650 - 106 = 544 10 cm.
Or x = 272 Example 11: The digit at the ten's place of a
two digit number is twice the digit at the unit's
Hence, the number of boys = 272
place. If the sum of this number and the
And, the number of girls = (x + 106) number formed by reversing the digits is 66.
= 272 + 106 = 378 Find the number .
Solution : Let the unit place digit = x
Example 9: The present age of Jacob's father is
three times that of Jacob. After 5 years, the Ten's place digit = 2x
difference of their ages will be 30 years. Find Number formed = 10(2x) + x = 20x + x = 21x
their present ages.
Reversing the digit :
Solution: Let the present age of Jacob be x
Unit digit = 2x
years.
Ten's digit = x
Therefore, the present age of his father is 3x
New number formed = 10 (x) + 2x
years.
= 10x + 2x
After 5 years, the age of Jacob = (x + 5) years.
= 12x
After 5 years, the age of his father = (3x + 5)
As the sum of the number is 66.
years.
21x + 12 x = 66
The difference of their ages = (3x + 5) - (x + 5)
33x = 66
years, which is given to be 30 years, therefore
x = 2
3x + 5 - (x + 5) = 30
So, unit digit = 2
or 3x + 5 - x - 5 = 30
Number = 21x
or 3x - x = 30
= 21(2)
or 2x = 30
Number = 42
or x = 15

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Mathematics In Focus - 8