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# Word Problems Hard

Below you will find 16 very hard word problems. Select the correct answers and press the answers button at the bottom of the page to obtain your score. A calculator or scrap paper may be used! Good luck!

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## Start the test!

 1 Leonardo is heading out again in his Bugatti Veyron. Once more he drives from Pisa to Milan, at an average 380 km/hour. It takes him 45 minutes. On the return journey he gets stuck in traffic. The traffic jam is 10 km long, and it takes him 1.5 hours to get through. After this he drives another 60km in slow moving traffic at 40 km/hour, after which Leonardo can resume his route as normal. In total his average speed on both trips measures 114 km/hour. What was his average speed on the return journey when he wasn’t stuck in a traffic jam or slow moving traffic?
 380 km/hour 172 km/hour 215 km/hour 133,3 km/hour
 2 Leonardo has 3 taps in his bath. If he only fully opens tap 1 it takes 10 minutes to fill the bath. If he only fully opens tap 2 it takes 15 minutes to fill the bath, and if he only fully opens tap 3 it takes 30 minutes to fill the bath. If Leonardo were to fully open all 3 taps how long would it take to fill the bath?
 5 min 10 min 3,4 min 7 min
 3 Leonardo wants to make Invar. Invar is an alloy with an extremely low expansion coefficiency, comprising 36% nickel and 64% iron. He has 20 kg of alloy comprising 20% nickel and 80% iron. And he has 180 kg of alloy comprising 50% nickel and 50% iron. How many maximum kilos of Invar can he make?
 54 kg 83 kg 23 kg 43 kg
 4 Leonardo keeps ostriches and sheep: in total 80 animals. Together all the animals have 220 legs. How many ostriches does he have?
 30 40 50 60
 5 An aeroplane flies 800 km with the wind behind it. With the same capacity and in the same time it would fly into the wind at 720 km. The wind speed is 30 km/hour. What is the speed of the aeroplane without wind?
 760 km/hour 42,5 km/hour 570 km/hour 770 km/hour
 6 Leonardo wants to construct an ostrich run with 100 m fencing. Using this fencing he wants to make an ostrich run with as big a surface area as possible. The type of fencing that he uses cannot bend; but he does have 4 right-angled (90°) corner pieces. What will the surface area of this ostrich run be?
 625 m2 2500 m2 100 m2 500 m2
 7 Leonardo usually pays € 0.50 for 3 pencils. He sells a pair for € 0.50. In one day Leonardo makes € 2.50 profit. How many pencils did he sell that day?
 30 40 50 60
 8 Leonardo divides € 14,000 out over 2 bank accounts. Bank account A earns 5% interest; bank account B 7%. At the end of the year Leonardo receives € 798. How much has Leonardo paid into bank account B?
 € 4.900,- € 9.100,- € 10.100,- € 5.100,-
 9 Leonardo takes part in a cycle race. He sets off at a good speed of 35 km/hour. Once Leonardo has ridden half the race (in distance) he realises he set off too quickly and reduces his speed to 25 km/hour. He finishes the race at this speed. In total it takes him 3 hours and 36 mins. What distance has Leonardo cycled?
 105 km 52,5 km 60 km 125 km
 10 Every Monday Leonardo cleans his toilet and every fifth day he vacuums. If today he is cleaning his toilet as well as vacuuming how long will it be before he cleans his toilet and vacuums on the same day again?
 70 days 7 days 35 days 25 days
 11 Leonardo has designed a solar panel. He uses some of the power he generates with this solar panel for personal use, and the rest he sells to his energy supplier. Within the space of a month Leonardo uses 390 m3 gas and sells 130 KWh electricity. His fuel bill for that month amounts to € 130. The following month he uses 360 m3 gas and sells 160 KWh electricity. His bill for that month amounts to € 110. How much does the energy supplier pay Leonardo for 1 KWh electricity?
 € 0,50 € 0,12 € 0,25 € 0,42
 12 Plato is approximately just as many days old as Aristotle is weeks old and Plato is just as many months old as Leonardo is years old. Together Plato, Aristotle and Leonardo are 140 years old. How old is Leonardo? (assume 1 year = 12 months = 52 weeks = 365 days)
 86 years 84 years 56 years 46 years
 13 For his mathematics exams Leonardo has to take 4 tests. He achieves a score of 9.4 and 9.8 in the first 2. What average score must he achieve for the next 2 is he wants to achieve an average score of 9.5? The 2 tests he still has to take together account for 25% of the final score.
 9,2 9,0 9,4 9,5
 14 Think of a 3 digit number that when you switch round the ten and hundred numbers the resulting number is 20% more than the original number.
 440 540 860 450
 15 Leonardo wants to place a bird cages in his garden. For this he has set aside 52 m2 of garden and € 825. Bird cage A has a capacity of 14 m3 and a ground area of 4 m2 and costs € 50. Bird cage B has a ground area of 8 m2, a capacity of 30 m3 and costs € 125. How many of each bird cage does he need to place in order to attain as large a bird cage content as possible; within his budget and allocated space? The bird cages cannot be stacked due to their fragile construction.
 Bird cage A: 3 pieces; Bird cage B: 5 pieces Bird cage A: 1 pieces; Bird cage B: 6 pieces Bird cage A: 13 pieces; Bird cage B: 0 pieces Bird cage A: 5 pieces; Bird cage B: 4 pieces
 16 Leonardo is 9 years younger than 3x as old Archimedes. 4 years ago he was 10 years older than 2x as old Archimedes. How old is Leonardo?
 56 years 15 years 44 years 36 years