The ratio of the marks obtained by Yash in English to Hindi is 15:16 and the marks obtained in maths to science is 5:6. The aggregate marks in 64% in the four subjects together. If the marks obtained in English and Maths are the same and the maximum marks in each subject are 100 then find the total marks obtained by him in Hindi and science together.
Question
The ratio of the marks obtained by Yash in English to Hindi is 15:16 and the marks obtained in maths to science is 5:6. The aggregate marks in 64% in the four subjects together. If the marks obtained in English and Maths are the same and the maximum marks in each subject are 100 then find the total marks obtained by him in Hindi and science together.
Solution
Let's solve the problem step by step:
Step 1: Let's assume the marks obtained in English and Maths are both x.
Step 2: According to the given ratio, the marks obtained by Yash in English to Hindi is 15:16. So, the marks obtained in Hindi can be calculated as (16/15) * x.
Step 3: Similarly, the marks obtained in Maths to Science is 5:6. So, the marks obtained in Science can be calculated as (6/5) * x.
Step 4: The aggregate marks in the four subjects together is 64%. So, the total marks obtained in all four subjects can be calculated as 0.64 * 400 (since the maximum marks in each subject is 100).
Step 5: Now, we can set up an equation to find the value of x. The equation is: x + x + (16/15) * x + (6/5) * x = 0.64 * 400.
Step 6: Simplifying the equation, we get: 15x + 15x + 16x + 18x = 0.64 * 400.
Step 7: Combining like terms, we get: 64x = 0.64 * 400.
Step 8: Dividing both sides of the equation by 64, we get: x = 0.64 * 400 / 64.
Step 9: Evaluating the expression, we get: x = 4.
Step 10: Now, we can calculate the marks obtained in Hindi and Science. The marks obtained in Hindi is (16/15) * x = (16/15) * 4 = 64/15.
Step 11: The marks obtained in Science is (6/5) * x = (6/5) * 4 = 24/5.
Step 12: Finally, we can find the total marks obtained by Yash in Hindi and Science together. It is (64/15) + (24/5) = (64/15) + (72/15) = 136/15.
Therefore, the total marks obtained by Yash in Hindi and Science together is 136/15.
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