Question
Download Solution PDFAverage of numbers A, B & C is 60. If the ratio of sum of A & B to that of C is 7 : 2, then find the value of B. Given that value of A is 20 more than B.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Average of A, B, and C = 60
The ratio of the sum of A and B to C is 7:2.
A is 20 more than B.
Calculation:
Average of A, B, and C = (A + B + C) / 3 = 60
A + B + C = 60 × 3 = 180
Also, we are given that (A + B) / C = 7 / 2. Therefore:
A + B = (7 / 2) × C
From A = B + 20, substitute this into the equation A + B = (7 / 2) × C:
(B + 20 + B) = (7 / 2) × C
2B + 20 = (7 / 2) × C
Now, we also know that A + B + C = 180. Substitute A = B + 20 into this equation:
(B + 20) + B + C = 180
2B + 20 + C = 180
C = 180 - 2B - 20
C = 160 - 2B
Now substitute C = 160 - 2B into the equation 2B + 20 = (7 / 2) × C:
2B + 20 = (7 / 2) × (160 - 2B)
2B + 20 = 560 - 7B
2B + 7B = 560 - 20
9B = 540
B = 540 / 9 = 60
∴ The value of B is 60.
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