Problem based on Ages Math Questions for competitive exams

  Problem based on Ages

 (उम्र पर आधारित समस्या)

 Ritu’s age after 6 years will be three–sevenths of her father’s age. 10 years ago, the ratio of their ages was 1 : 5.What is Ritu’s father’s age at present? 

6 साल बाद रितु की उम्र उसके पिता की उम्र का तीन-सातवां हिस्सा होगी। 10 वर्ष पहले, उनकी आयु का अनुपात 1:5 था। वर्तमान में रितु के पिता की आयु क्या है?

Solution: Let Ritu’s age 10 years ago be x years.

Then, her father’s age 10 years ago = 5x years. 

⇒(x+10)+6= 3⁄7 [(5x+10)+6]

⇒x+16= 3⁄7(5x+16)

c

 ⇒ 7x + 112 = 15x + 48 

 ⇒ 8x = 64 

 ⇒ x = 8.

∴ Ritu’s father’s present age = (5x + 10) = (5 × 8 + 10) years = 50 years.

Type-1

The age of father 3 years ago was 7 times the age of his son. At present the father's age is 5 times that of his son what are the present age of the father &  the son ?

Solution: Let the present age of the son = x yrs

Then the present age of the father = 5x yrs

3 yrs ago

    7(x-3)=5x-3

 ⇒7x-21=5x-3

 ⇒7x-5x=21-3

 ⇒2x=18

 ⇒x=9yrs

Therefore the son's age=9 yrs & the father's age=(5 X 9)yrs

                                                                                  =45yrs

Quicker Method:

Son's Age= ³⁽⁷⁻¹⁾⁄₇₋₅

              = 3x6 / 2

              =9 yrs

Type-2

At present the father's age is 5 times that of his son .After 3 years father's age would be 4 times that of his son what are the present age of the father &  the son ?

Solution : Let the present age of the son = x yrs

Then the present age of the father = 5x yrs

3 years After

⇒4(x+3)=5x+3

⇒4x+12=5x+3

⇒4x-5x=3-12

⇒-x= - 9

⇒x= 9 yrs

Therefore the son's age=9 yrs & the father's age=(5 X 9)yrs

                                                                                  =45yrs

Quicker Method:

Son's Age = 3(4-1) ⁄ (5-4)

           =(3x3)/1

           =9 yrs