An employer reduces the number of his employees in the ratio 9 : 8 and increases their wages in the ratio 14 : 15. If the original wage was Rs. 18,900, then find the ratio of the old wage bill to the new one.

Let the initial number of employees be 9x and the initial wage per employee be 14y, where the original wage of 18900 helps establish a baseline but the total wage bill ratio can be found using the component ratios directly. The old wage bill is proportional to 9 * 14 = 126. The new wage bill is proportional to the new number of employees, 8x, multiplied by the new wage, 15y, giving 8 * 15 = 120. The ratio of the old wage bill to the new one is 126 : 120, which simplifies to 21 : 20. The required ratio is 21 : 20.

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