A shopkeeper sells milk. He marks up the price of milk to 60% above its cost price and offers a discount of 20% on the marked price upon selling it. If the shopkeeper cheats his customer by selling 'y' ml less in every 1 litre pack of milk, he earns a profit of Rs. 2160 on selling 12 litres of milk. If 1 litre of milk is sold honestly without cheating in quantity, then the difference between the discount given and the profit earned is Rs. 20. Find the value of (4y + 20).

Let the cost price of 1 litre of milk be Rs. 100m

Marked price of 1 litre of milk = 100m × 1.6 = Rs. 160m

Selling price of 1 litre of milk = 160m × 0.8 = Rs. 128m

Profit without cheating = 128m - 100m = Rs. 28m

Discount given = 160m - 128m = 32m

ATP,

32m - 28m = 20

Or, 4m = 20

So, m = 5

Cost price of 1 litre of milk = 100 × 5 = Rs. 500

Selling price of 1 litre of milk = 128 × 5 = Rs. 640

Selling price of (1000 - y) ml of milk = Rs. 640

Profit earned on selling 12 packets of (1000 - y) ml milk = Rs. 2160

So, profit earned on selling (1000 - y) ml milk = 2160 ÷ 12 = Rs. 180

So, cost price of (1000 - y) ml milk = 640 - 180 = Rs. 460

(460/500) = {(1000 - y)/1000}

0.92 × 1000 = 1000 - y

So, y = 1000 - 920 = 80

Therefore, required value = 4y + 20 = 320 + 20 = 340