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Ghanshyam and Raju got their marks(out of 50 marks) in 4 subjects i.e English, Science, Maths and Social. The avg marks obtained by Raju is 38. The ratio of marks obtained by Raju and Ghanshyam in Maths is 5 ∶ 6 and the average marks obtained by Ghanshyam is 41. If the marks scored by both of them in English and Science is same and in Social Raju got 5 marks less than Ghanshyam. What is the marks scored by them in English and Science if Raju scored 40 marks in Social?

Ghanshyam and Raju got their marks(out of 50 marks) in 4 subjects i.e English, Science, Maths and Social. The avg marks obtained by Raju is 38. The ratio of marks obtained by Raju and Ghanshyam in Maths is 5 ∶ 6 and the average marks obtained by Ghanshyam is 41. If the marks scored by both of them in English and Science is same and in Social Raju got 5 marks less than Ghanshyam. What is the marks scored by them in English and Science if Raju scored 40 marks in Social? Correct Answer 38.5

Total marks scored by Raju = 38 × 4 = 152

Total marks scored by Ghanshyam  = 41 × 4 = 164

Ratio of marks obtained by Raju and Ghanshyam in Maths = 5 ∶ 6

⇒ Let the marks obtained by Raju and Ghanshyam in Maths be 5x and 6x

Marks scored by Raju in Social = 40

Marks scored by Ghanshyam in Social = 45

Let the marks scored by them in English and Science = y

∴ The difference in marks scored by them 

⇒ (6x + y + y + 45) – (5x + y + y + 40) = 164 – 152

⇒ x = 7

∴ Marks scored by Raju in Maths = 7 × 5 = 35

∴ Marks obtained by Raju in English and Science 

⇒ y + y = 152 – 40 – 35 = 77

⇒ y = 77/2 = 38.5

∴ The marks scored by Ghanshyam and Raju in English and Science is 38.5

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