Arithmetic, Mental Math and Unit Conversion | Shopping, Percentages and Time Problems, Set 1
Problem 1
You buy three items at 238 yen each and one drink at 165 yen, and pay with a 1,000-yen note. How much change do you get?
View explanation
Three items come to 238 × 3 = 714 yen, and adding the drink gives 714 + 165 = 879 yen. The change is therefore 1,000 − 879 = 121 yen. The figure 286 is 1,000 − 714 without the drink, and 879 is the total price rather than the change.
Problem 2
What is 2.35 km expressed in meters?
View explanation
1 km is 1,000 m, so 2.35 × 1,000 = 2,350 m. The figure 235 m multiplies by 100 instead of the 1,000 needed to convert km to m, while 23,500 m has one digit too many.
Problem 3
A container holds 1.8 L of water. If 250 mL is added, how many milliliters of water are there in total?
View explanation
1 L is 1,000 mL, so 1.8 L is 1,800 mL. Working in the same unit, 1,800 + 250 = 2,050 mL. The figure 1,800 mL omits the 250 mL added, and 2,250 mL treats the 1.8 L as 2 L.
Problem 4
You buy an item listed at 6,400 yen with a 15% discount. How much do you pay?
View explanation
The discount is 6,400 × 0.15 = 960 yen, so the amount paid is 6,400 − 960 = 5,440 yen. The figure 960 yen is the discount, not the amount paid. The figure 6,385 yen mistakes "15%" for 15 yen and subtracts just 15 from the list price.
Problem 5
Of those who registered for a training course, 70% — 84 people — attended on the day. How many registered in total?
View explanation
Taking the number who registered as the base, 70% of it is 84, so the number is 84 ÷ 0.70 = 120. The figure 59 is 84 × 0.70 = 58.8 rounded, applying 70% again to a figure that already has the percentage applied. The figure 280 wrongly divides by the 30% who did not attend.
Problem 6
You plan to buy three items at 1,980 yen, 3,040 yen and 4,970 yen. Rounding each price to the nearest thousand yen, what is the estimated total?
View explanation
Rounded to the nearest thousand, 1,980 becomes 2,000, 3,040 becomes 3,000 and 4,970 becomes 5,000. The estimate is therefore 2,000 + 3,000 + 5,000 = 10,000 yen. The figure 9,990 yen is the exact total, not the estimate the question asks for, and 8,000 yen rounds each price down.
Problem 7
You cycle 18 km at a constant 12 km/h. How many minutes does it take?
View explanation
Time is distance ÷ speed, so 18 ÷ 12 = 1.5 hours. An hour is 60 minutes, so 1.5 × 60 = 90 minutes. The figure 216 comes from 18 × 12, multiplying distance by speed. The 0.5 in 1.5 hours is 30 minutes, not 50.
Problem 8
A dish for four people uses 300 g of flour. How many grams are needed for ten people at the same amount per person?
View explanation
One person's share is 300 ÷ 4 = 75 g, so ten people need 75 × 10 = 750 g. The figure 600 g doubles the 300 g, which would serve only eight. The figure 3,000 g mistakes the 300 g for four people as one person's share and multiplies it by ten.
Problem 9
You are catching a train that departs at 8:42. You want to be on the platform at least 5 minutes before it leaves. It takes 12 minutes to walk from home to the station entrance, and 3 minutes to collect a reserved ticket from the machine at the entrance. By what time must you leave home at the latest?
View explanation
Being on the platform 5 minutes before 8:42 means 8:37. Subtracting the 3 minutes at the ticket machine puts arrival at the station entrance at 8:34, and subtracting the 12-minute walk means leaving by 8:22. The answer 8:25 ignores the 3 minutes at the machine, and 8:27 ignores the 5-minute margin before departure.
Problem 10
From 2.5 kg of beans, the 12% that are of poor quality are removed. Packing the rest into bags of 180 g each, how many bags can be filled completely at most, and how many grams are left over?
View explanation
The share remaining is 100% − 12% = 88%, so 2.5 × 0.88 = 2.2 kg, that is 2,200 g. Since 2,200 ÷ 180 = 12 remainder 40, 12 bags can be filled completely with 40 g left over. Thirteen bags would need 2,340 g, which is more than there is. The answer of 12 bags with 340 g left over comes from subtracting only 2,160 g from the original 2,500 g.