# Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

1) The sum of 5 consecutive numbers is 465. What is the smallest number?

Ans :- 91.

2) A farm has some ducks and cows. The ratio of the number of animals to the total number of legs is 8 : 23. Express the number of ducks as a fraction of the cows.
Give your answer in the simplest form.

Ans :- 127.

3) There were a total of 4540 passengers onboard 4 ships, labeled A, B, C and D. All the ships were travelling on different sea routes. Ship A had the most number of passengers onboard and Ship D had the least. The difference in the number of passengers onboard Ship A and the other three ships was 139, 363 and 618.
(a) How many passengers were onboard Ship D?
(b) Each ship was required to load sufficient lifeboats to carry all its passengers onboard in case of emergency. Each lifeboat could take up to 30 passengers. Find the total minimum number of lifeboats to be loaded on Ship A and Ship D.

Ans :- a) 797
b) 75 .

4) Kerry took an empty container and filled it with 185 mℓ of oil. The next day, she filled the container with as much oil as the amount that was in it the day before. Every day, she repeated this and after the 5th day, the container was 80% full. What was the capacity of the container in litres?

Ans :- 3.7 ℓ.

5) Polly, Queenie and Remmy were given an equal number of charity tickets to sell. However, none of them completed selling their share of tickets. Polly sold 6 times as many tickets a Queenie and was left with 12 unsold tickets. 13 of the tickets sold by Remmy was 3 more than those sold by Queenie. The three of them sold a total of 239 tickets. How many charity tickets did each of them receive?

Ans :- 150 .

6) 79 of Maria's savings was twice of Adele's savings. The ratio of Adele's savings to Safia's is 14 : 5. How much was Maria's savings if the 3 girls have a total of \$3080?

Ans :- \$2016.

7) A contractor needed to cover an entire hall with tiles. On the first day, he laid 319 tiles. He completed tiling the rest of the hall in 7 days using an equal number of tiles each day. At the end of the 4th day, he was able to tile 815 of the hall. How many tiles did the contractor use to cover the whole hall?

Ans :- 1740 .

8) 35 pupil leaders from a primary school were asked to welcome visitors during the schools opening ceremony. They were stationed in a row from one end of the school's entrance to the other end at an equal spacing of 1.3 m apart. On the day of the opening ceremony, 8 pupils did not turn up. As a result, the remaining pupil leaders were restationed at a new equal spacing. What was the new spacing between 2 pupil leaders?

Ans :- 1.7 m.

9) Raju has solved 260 Math problems to prepare for his mid year examinations. He planned to finish the rest of the Math problems in the next 6 days by solving the same number of Math problems each day. If he completed 32% of the Math problems in the next 4 days, how many Math problems would he have solved altogether?

Ans :- 500.

10) At a carnival, there were 40% more males than females. There was an equal number of males without caps to the number of females without caps. The number of males with caps to the number of females with caps was 6 : 2.
(a) What was the ratio of the number of females with caps to the number of females without caps?
(b) Midway, 800 females left the carnival. In the end, there were 37as many females as males
remaining behind. How many people were at the carnival at first?

Ans :- a) 1 : 4
b) 4800 .