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Hi

The questions sent periodically by email to TOPGRE's Yahoo group subscribers will also be posted on the forum along with explanatory answer that will follow. Here is the first of the questions

Question
If the ratio of the ages of two friends A and B is in the ratio 3 : 5 and that of B and C is 3 : 5 and the sum of their ages is 147, then how old is B?

1. 15 years
2. 75 years
3. 49 years
4. 45 years
5. 27 years

45. Option 4 is correct.

Is that right?

Can you please explain how you got the answer?

B is common to both the ratios.

In the first ratio A : B is 3 : 5 and in the second one B : C is 3 : 5.

So, equate the value of B in both the ratios to be same. This can be done by taking the LCM of the values of B in both the ratios.

LCM of values of B in both the ratios is the LCM of 5 and 3 = 15.

So, the first ratio A : B 3 : 5 can be written as 9 : 15 by multiplying it by '3'
The second ratio B : C 3 : 5 can be witten as 15 : 25 by multiplying it by '5'.

Therefore, now we can combine the ratios as A : B : C = 9 : 15 : 25 as the value of B in both the ratios are now equal.

NOw it is a straight forward ratio question with the sum of ages being 9x + 15x + 25x = 49x = 147 and hence x = 3.

Therefore, age of B = 15x = 15 * 3 = 45