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Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7:9, how old is Sachin? A. 16 years B. 18 years C. 28 years D. 24.5 years E. none of these

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
A. 16 years
B. 18 years
C. 28 years
D. 24.5 years
E. none of these

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Assume the age of Sachin as ‘x’. Thus get the age of Rahul and form of relation connecting their present ages to 7:9. Use cross product property and find the value of x. Complete step-by-step answer: Let us assume the age of Sachin as ‘x’. It is said that Rahul is 7 years older than Sachin. Therefore the age of Rahul is (x + 7). Now the ages of Sachin and Rahul are given in the ratio 7:9. Thus we can say that x:x+7=7:9 . Thus we can say that x:x+7=7:9 . We can also write it as, xx+7=79 . Now using cross product we can write that, 9x=7(x+7)9x=7x+49 Now let us rearrange them and find the value of x. 2x=49x=492=24.5 Thus the age of Sachin = x = 24.5 Age of Rahul = x + 7 = 24.5 +7 = 31.5 What we need is the age of Sachin which is 24.5 Thus we got the age of Sachin as 24.5 years. Option D is the correct answer. Note:We can take the age of Rahul as ‘x’ and that of Sachin as x-7. Thus the ratio becomes, x−7:x=7:9 , which can also be written as, x−7x=79⇒9(x−7)=7x9x−63=7x∴x=63/2=31.5 Thus the age of Rahul = x = 31.5 years. Age of Sachin = x – 7 = 31.5 – 7 = 24.5 years.

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