Ananthu's and Malay's ages 5 years ago were in the ratio 4:5. 15 years hence, their age ratio will become
6:7. What was Ananthu's age 10 years before?
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Ananthu's and Malay's ages 5 years ago were in the ratio 4:5. 15 years hence, their age ratio will become
6:7. What was Ananthu's age 10 years before?
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Answer:
Step-by-step explanation:
Given :-
Ananthu's and Malay's ages 5 years ago were in the ratio 4:5. 15 years hence, their age ratio will become 6:7.
To find:-
What was Ananthu's age 10 years before?
Solution:-
Let the present age of Ananthu be X years
and the age of Malay be Y years
5 years ago ,their ages will be (X-5) and (Y-5) years respectively.
Their ratio is 4:5
=>(X-5):(Y-5)= 4:5
=>(X-5)/(Y-5)=4/5
applying cross multiplying
=>5(X-5)=4(Y-5)
=>5X-25=4Y-20
=>5X=4Y-20+25
=>5X=4Y+5
=>X=(4Y+5)/5........(1)
and After 15 years their ratio becomes 6:7
=>(X+15):(Y+15)=6:7
=>(X+15)/(Y+15)=6/7
=>7(X+15)=6(Y+15)
=>7X+105=6Y+90
=>7X-6Y=90-105
=>7X-6Y= -15.....(2)
Substituting the value of X in (2) then
=>[7(4Y+5)/5]-6Y=-15
=>(28Y+35-30Y)/5=-15
=>(-2Y+35)=-15×5
=>-2Y+35=-75
=>-2Y=-75-35
=>-2Y=-110
=>Y=-110/-2
=>Y=55 years
and X=[4(55)+5]/5
=>X=(220+5)/5
=>X=225/5
=>X=45 years
Ananthu's age 10 years before=X-10
=45-10=35 years
Answer:-
Ananthu's age before 10 years was 35 years
Let the present age of Ananthu and Malay be x and y respectively.
5 years ago:
Age of Ananthu = x-5
Age of Malay = y-5
We know that the ratio of ages are 4:5 :-
Cross multiplying and further simplifying this equation, we get:
________(1)
15 years hence:
Age of Ananthu = x+15
Age of Malay = y+15
We know that the ratio of ages are 6:7 :-
Cross multiplying and further simplifying this equation, we get:
________(2)
So, we get two equations:
Multiply 3 to the first equation and 2 to the second equation. You will get:
Now, subtract these equations. You will get:
∴Ananthu's present age is 45 years.
Age before 10 years ⇒ 45-10 ⇒ 35 years.
Ananthu's age 10 years before is 35 years.