Arithmetic Word Problems Flashcards

A 40-liter mixture of milk and water is in a ratio of 3:1. How many liters of water must be added to make the ratio 2:1?

Answer: 5 liters

Milk = 30 L, water = 10 L; 30 ÷ (10 + x) = 2 → 30 = 20 + 2x → x = 5 liters.

A factory has 15 workers who can complete an order in 8 days. After 2 days, 5 workers are transferred away. How many more days are needed to finish?

Answer: 9

Total work = 120 unit-days; done = 30; remaining = 90; 10 workers need 90 ÷ 10 = 9 more days.

A merchant sells two items for $990 each — gaining 10% on one and losing 10% on the other. What is the overall result?

Answer: Loss of $20

CP₁ = $990 ÷ 1.10 = $900; CP₂ = $990 ÷ 0.90 = $1,100; total CP = $2,000, SP = $1,980; net loss = $20.

A cyclist rides 3 km at 12 km/h and then 6 km at 9 km/h. What is the total time taken, in minutes?

Answer: 55 min

Time 1 = 3 ÷ 12 = 0.25 h = 15 min; Time 2 = 6 ÷ 9 = 40 min; total = 55 min.

A bag of apples weighs 3.6 kg. Each apple weighs approximately 120 grams. About how many apples are in the bag?

Answer: 30

3,600 g ÷ 120 g = 30 apples.

A printer finishes a job in 6 hours. After it works alone for 4 hours, an assistant takes over and finishes the remaining work in 4 hours. How long would the assistant take to do the entire job alone?

Answer: 12 hours

Printer completes 4/6 = 2/3 of the job; remaining 1/3 is done by the assistant in 4 hours, so the assistant's full job time = 4 ÷ (1/3) = 12 hours.

A store reduces prices by 25% for a sale, then raises prices by 25% after the sale. What is the net change from the original price?

Answer: 6.25% decrease

Starting at $100: after −25% = $75; after +25% = $93.75; net change = −6.25%.