Given information:
Consumer Price Index (CPI) for April 1985 = 125
Food Price Index = 120
Other Items Index = 135

We need to find the percentage of the total weight of the index.

Total weight of the index = (Weight of Food Price Index) + (Weight of Other Items Index)

To calculate the weight of each index, we need to use the Laspeyres formula:

Weight of Food Price Index = (Price of Food Items in the base year × Quantity of Food Items in the current year) ÷ (Price of Food Items in the base year × Quantity of Food Items in the base year) × 100

Weight of Other Items Index = (Price of Other Items in the base year × Quantity of Other Items in the current year) ÷ (Price of Other Items in the base year × Quantity of Other Items in the base year) × 100

Let's assume that the base year is 1984.

According to the question, CPI for April 1985 = 125
Therefore, the price level in 1985 is 125/100 = 1.25 times the price level in 1984.

Let's assume that the total expenditure in 1984 on food items and other items was Rs. 100.

Price of Food Items in 1984 = Rs. 50
Quantity of Food Items in 1984 = 2 units
Price of Other Items in 1984 = Rs. 50
Quantity of Other Items in 1984 = 2 units

Price of Food Items in 1985 = 1.25 × Rs. 50 = Rs. 62.50
Quantity of Food Items in 1985 = 3 units
Price of Other Items in 1985 = 1.25 × Rs. 50 = Rs. 62.50
Quantity of Other Items in 1985 = 3 units

Using the Laspeyres formula, we can calculate the weight of each index:

Weight of Food Price Index = (Rs. 50 × 3) ÷ (Rs. 50 × 2) × 100 = 150/100 = 1.5
Weight of Other Items Index = (Rs. 50 × 3) ÷ (Rs. 50 × 2) × 100 = 150/100 = 1.5

Total weight of the index = 1.5 + 1.5 = 3

Percentage of the total weight of the index = (Total weight of the index ÷ 2) × 100 = (3 ÷ 2) × 100 = 66.67%

Therefore, the correct option is (a) 66.67.