If the ratio of the ages of two friends A and B is 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?
If the ratio of the ages of two friends A and B is 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?
The correct option is C 45
The ratio of the ages of A and B is 3 : 5. The ratio of the ages of B and C is 3 : 5. B's age is the common link to both these ratios. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio. The can be done by getting the value of B in both ratios to be the LCM of 3 and 5, i.e., 15. The first ratio between A and B will, therefore, be 9 : 15 and the second ratio between B and C will be 15 : 25. Now combining the two ratios, we get A : B : C = 9 : 15 : 25. Let their ages be 9x, 15x and 25x. Then, the sum of their ages will be 9x + 15x + 25x = 49x. The question states that the sum of their ages is 147, i.e., 49x = 147 or x = 3. Therefore, B's age = 15x = 15×3 = 45
45
The ratio of the ages of A and B is 3 : 5. The ratio of the ages of B and C is 3 : 5. B's age is the common link to both these ratios. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio. The can be done by getting the value of B in both ratios to be the LCM of 3 and 5, i.e., 15. The first ratio between A and B will, therefore, be 9 : 15 and the second ratio between B and C will be 15 : 25. Now combining the two ratios, we get A : B : C = 9 : 15 : 25. Let their ages be 9x, 15x and 25x. Then, the sum of their ages will be 9x + 15x + 25x = 49x. The question states that the sum of their ages is 147, i.e., 49x = 147 or x = 3. Therefore, B's age = 15x = 15×3 = 45
