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Sam and Raju scored 52% and 61% respectively in the Term 1 examination. In the Term 2 examination, Sam scored 50% more than Raju. If the total marks scored by Sam and Raju are the same, then what is the ratio of marks scored by Sam in the Term 1 examination to the Term 2 examination?

Sam and Raju scored 52% and 61% respectively in the Term 1 examination. In the Term 2 examination, Sam scored 50% more than Raju. If the total marks scored by Sam and Raju are the same, then what is the ratio of marks scored by Sam in the Term 1 examination to the Term 2 examination? Correct Answer 52 : 27

Calculation:

Let M be the maximum score in the Term 1 examination.

Sam scored = (52/100) × M = 0.52M

Raju scored = 0.61M

Let r be the marks scored by Raju in the Term 2 examination.

Sam scored = (150/100) × r = 1.5r

Total marks scored by Sam = 0.52M + 1.5r

Total marks scored by Raju = 0.61M + r

⇒ 0.52M + 1.5r = 0.61M + 1r

⇒ 0.5r = 0.09M

⇒  r = 0.18M

Marks scored by Sam In Term 2 = 1.5 r = 1.5 × 0.18 M = 0.27M

The ratio is 0.52M : 0.27M.

The ratio is 52 : 27.

Important Points

If there are two similar quantities (e.g. Marks or Volume) try to find the relation between those quantities will solve most of the problems.

Wisely choose the variables (for example - using a variable for maximum marks scored in the term 2 will not be helpful)

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