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Q.

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages and choose the option which follows.


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a

Rakhi’s age is 20 years and her mother’s age is 40 years.

b

Rakhi’s age is 10 years and her mother’s age is 40 years.

c

Rakhi’s age is 10 years and her mother’s age is 50 years.

d

Rakhi’s age is 5 years and her mother’s age is 30 years. 

answer is A.

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Detailed Solution

detailed_solution_thumbnail
It is given that Rakhi’s mother is four times her daughter. And, after 5 years, Rakhi’s mother becomes 3 times as old as she was before.
Now, assume the present age of Rakhi to be x years.
As Rakhi’s mother is four times as old as Rakhi, so, present age of Rakhi’s mother will be 4x years.
Next, after 5 years, Age of Rakhi = (x+5) years
The age of Rakhi’s mother = (4x+5) years.
So, according to the condition, we can set up an equation as follows,
4x+5=3(x+5) 4x+5=3x+15
4x+5−3x=3x+15−3x −x+5=15 −x+5−5=15−5 −x=−10
−x −1 = −10 −1
x=10
So, the age of Rakhi at present is 10 years.
Then, her mother’s age will be,
4×10=40 years.
Hence, the age of Rakhi at present is 10 years and her mother’s age is 40 years.
Hence, the correct option is (1).
 
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