A man bought 20 liters of milk at sh.1500 per liter. On his way back home, some milk spilled, and he sold the remaining milk at sh.1200 per half liter and made a profit of 20%. How much milk spilled?

Let's first calculate the total cost of the 20 liters of milk:

Cost of 20 liters of milk = 20 liters * sh.1500 per liter = sh.30,000

Now, let's calculate the selling price of the remaining milk after some spilled:

Profit made = 20% of sh.30,000 = 0.2 * sh.30,000 = sh.6,000

Total selling price = Cost price + Profit = sh.30,000 + sh.6,000 = sh.36,000

He sold the remaining milk at sh.1200 per half liter, which means sh.2400 per liter.

Remaining milk sold = sh.36,000 / sh.2400 per liter = 15 liters

So, the amount of milk that spilled = 20 liters - 15 liters = 5 liters

Therefore, 5 liters of milk spilled.

Step 1: Calculate the cost of 20 liters of milk

Cost of 20 liters = 20 x sh.1500 = sh.30,000

Step 2: Calculate the total selling price of the milk

Since the remaining milk was sold in half-liter units, the number of half-liter units is:

20 liters x 2 half-liters/liter = 40 half-liters

Selling price per half-liter = sh.1200

Total selling price = 40 x sh.1200 = sh.48,000

Step 3: Calculate the profit

Profit = Selling price - Cost price
= sh.48,000 - sh.30,000
= sh.18,000

Step 4: Calculate the percentage profit

Percentage profit = Profit / Cost price x 100
= 18,000 / 30,000 x 100
= 60%

Step 5: Calculate the original quantity of milk

Since the man made a 20% profit, the original quantity of milk was:

Profit percentage = (Selling price - Cost price) / Cost price x 100
0.2 = (48,000 - 30,000) / 30,000
0.2 = 18,000 / 30,000

Original quantity of milk = Cost price / (1 - Profit percentage)
= 30,000 / (1 - 0.2)
= 30,000 / 0.8
= 37,500 liters

Step 6: Calculate the amount of milk that spilled

Spilled milk = Original quantity of milk - Remaining quantity of milk
= 37,500 liters - 20 liters
= 17,500 liters

Therefore, the man spilled 17,500 liters of milk.

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