GCAT Arithmetic Word Problems 5 — Questions and Answers
Question 1: 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?
- 3 liters
- 5 liters (Correct answer)
- 7 liters
- 10 liters
Correct answer: 5 liters
Milk = 30 L, water = 10 L; 30 ÷ (10 + x) = 2 → 30 = 20 + 2x → x = 5 liters.
Question 2: 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?
- 7
- 9 (Correct answer)
- 12
- 15
Correct answer: 9
Total work = 120 unit-days; done = 30; remaining = 90; 10 workers need 90 ÷ 10 = 9 more days.
Question 3: A merchant sells two items for $990 each — gaining 10% on one and losing 10% on the other. What is the overall result?
- No profit or loss
- Loss of $20 (Correct answer)
- Profit of $20
- Loss of $9
Correct 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.
Question 4: 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?
- 45 min
- 50 min
- 55 min (Correct answer)
- 60 min
Correct answer: 55 min
Time 1 = 3 ÷ 12 = 0.25 h = 15 min; Time 2 = 6 ÷ 9 = 40 min; total = 55 min.
Question 5: A bag of apples weighs 3.6 kg. Each apple weighs approximately 120 grams. About how many apples are in the bag?
- 25
- 30 (Correct answer)
- 35
- 40
Correct answer: 30
3,600 g ÷ 120 g = 30 apples.
Question 6: 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?
- 8 hours
- 10 hours
- 12 hours (Correct answer)
- 16 hours
Correct 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.
Question 7: 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?
- No change
- 6.25% decrease (Correct answer)
- 6.25% increase
- 12.5% decrease
Correct answer: 6.25% decrease
Starting at $100: after −25% = $75; after +25% = $93.75; net change = −6.25%.
GCAT Arithmetic Word Problems 5
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?