Question
In a clothing store, the ratio of shirts to trousers to
T-shirts is 2:6:5. After Y trousers are sold, the ratio of shirts to trousers changes to 4:9. Then, after an additional 400 trousers are sold (making it Y + 400 trousers sold in total), the ratio of trousers to T-shirts becomes 1:2.Solution
Let the initial number of shirts, trousers and T-shirts in the store are 2n, 6n and 5n respectively.
When Y trousers sold from the store, then remaining number of trousers = 6n - Y
And 4: 9 = (2n): (6n - Y)
12n - 2Y = 9n
3n = 2Y
n = 2Y/3
When Y + 400 more trousers sold from the store, then remaining number of trousers = 6n - Y - (Y + 400) = 6n - 2Y - 400
And 1: 2 = (6n - 2Y - 400): (5n)
5n = 12n - 4Y - 800
4Y + 800 = 7n
4Y + 800 = 7 * 2Y/3
2Y/3 = 800
Y = 1200
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