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A library has two racks whose capacity ratio is 1 ∶ 2 and contains Engineering and Finance books only. The ratio of total Engineering and Finance books in two racks together is 2 ∶ 3 and the ratio of total Engineering and Finance books in smaller rack is 4 ∶ 5, then find the ratio of total Engineering and Finance larger rack.

A library has two racks whose capacity ratio is 1 ∶ 2 and contains Engineering and Finance books only. The ratio of total Engineering and Finance books in two racks together is 2 ∶ 3 and the ratio of total Engineering and Finance books in smaller rack is 4 ∶ 5, then find the ratio of total Engineering and Finance larger rack. Correct Answer 17 ∶ 28

Suppose total books in two racks = 270

Since the ratio of capacity of racks is 1 ∶ 2;

∴ Number of books in smaller rack = 1/3 × 270 = 90

Number of books in larger rack = 2/3 × 270 = 180

Since the ratio of total Engineering and Finance books in two racks together is 2 ∶ 3;

∴ Number of Engineering books in two racks together = 2/5 × 270 = 108

Number of Finance books in two racks together = 3/5 × 270 = 162

Since the number of books in the smaller rack is 90 and the ratio of total Engineering and Finance books in smaller rack is 4 ∶ 5;

∴ Number of Engineering books in smaller rack = 4/9 × 90 = 40

Number of Finance books in smaller rack = 5/9 × 90 = 50

∴ Number of Engineering books in larger rack = 108 - 40 = 68

Number of Finance books in larger rack = 162 - 50 = 112

∴ Required ratio = 68 ∶ 112 = 17 ∶ 28

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