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Question
The total age of 23 boys and 32 girls is 573 years while that of 32 boys and 23 girls is 582 years. Find the average age of a boy and a girl respectively.
Options
10, 11
12, 14
11, 10
None of these
MCQ
Solution
11, 10
Explanation:
Let average age of a boy = x and a girl = y
23x + 32y = 573
32x + 23y = 582
Here the coefficients of x and y are interchanged, in such cases a faster method of solving the equation is by adding and subtracting the equations.
Adding 55x + 55y = 1155
x + y = 21 .....(i)
Subtracting 9y – 9x = – 9
x – y = 1 ......(ii)
From (i) and (ii)
2x = 22, x = 11, y = 10
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Algebra (Entrance Exam)
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