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1 2
Example 15: Divide 36 into two parts in such a way that rd of one part is equal to rd of the other.
3 3
Solution: Let one part be x.
∴ Another part = (36 – x)

According to the question,
1 of one part = 2 of other part

3 3
1 2 1 2
⇒ of x = (36 – x) ⇒ x = (36 – x)
3 3 3 3
1 72 − 2x
⇒ x =
3 3
Multiply both sides by 3, we get

2 
 1   72 − x
3 ×  3    3 
x = 3



∴ x = 72 – 2x ⇒ x + 2x = 72
72
⇒ 3 x = 72 ⇒ x = = 24
3
∴ The 2nd part of the number = 36 – 24 = 12
Thus, the required two parts of 36 are 24 and 12.

Example 16: Naman’s present age is half the present age of his mother. Ten years ago, the mother
was thrice as old as Naman. What are their present ages?
Solution: Let the present age of Naman’s mother be n years.

1
Since Naman’s age is half the present age of his mother, therefore, the present age of Naman = n years.
2

Ten years ago, the age of Naman’s mother = (n – 10) years and the age of Naman =    1 n − 10 years.


2
According to the question,
1
( n – 10) = 3    2 n − 10 


3 Think and Answer
⇒ n – 10 = n – 30
2 1. Fifteen years from now, Ravi’s
Multiplying both sides by 2, we get age will be four times of his

2n – 20 = 3n – 60 present age. What is Ravi’s
present age?
⇒ 2n – 3n = –60 + 20 2. How many years old is a

⇒ –n = –40 or n = 40 person, if her age now is equals
to her age in 3 years × 3, less
Thus, the present age of Naman’s mother = 40 years 3 times her age 3 years ago?

 1 
and the present age of Naman =   2 × 40 years = 20 years.


Mathematics-8 44