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Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

1. There were 80 marbles in jars A, B and C altogether. Ahmad moved 4 marbles from A to B, 12 marbles from B to C and 2 marbles from C to A. The ratio of the number of marbles in B the number of marbles in C then become 3:5 with C having 58 as many marbles as A. What was the ratio of the number of marbles in A to that in B to that in C at first?

Ans :- 42 : 23 : 14.

2. In the construction of a highway, 2 km more than half of it was built in the first month. In the second month, 1 km less than ½ of the remaining highway were completed 20 km more of the highway were needed to be build to complete it. How long was the highway?

Ans :- 80 km.

3. At Mark's birthday party, 20% of the guests drank coke. 80 of the coke drinker were males. The remaining 38 of the coke-drinkers were females. For the rest of the guests who drank sprite, 352 were females and the rest were males. What percentage of the total number of guests was male who drank sprite?

Ans :- 25 % of the total number of guests was male who drank sprite.

4. Michelle left town A at 3:20 pm. 7 min later, she caught up with Jennifer who had left town A at an earlier time. Michelle eventually arrived at town B at 4:20 pm and her average speed for the whole journey was 60 km/h. Jennifer reached town B at 5:13 pm. What time did Jennifer leave town A, assuming that her average speed remains the same throughout the journey?

Ans :- Jennifer left Town a at 3:13 pm.

5. Kenny travelled at a speed of 60 km/h and Sally travelled at a speed of 40 km/h. Both of them started at 9:30 am at the same place but in opposite direction. After 45 min, Kenny turned back and decided to overtake Sally. At what time did Kenny overtake Sally?

Ans :- At 2 pm Kenny overtake Sally.

6. Ali and his cousin started cycling together at the same time from the same starting point. Ali cycled at an average speed of 15 km/h and reached the finishing line at 11 am. His cousin cycled at an average speed of 10 km/h and crossed the finishing line 2 hours later. Find the distance between the starting and the finishing line.

Ans :- 60 km.

7. At a wedding dinner, Chinese tea is served either in a glass or a cup. The amount of Chinese tea prepared is enough to fill up 84 glasses or 112 cups. If the waiter has already served 39 glasses and 35 cups of Chinese tea, how many more cups of Chinese tea can be served?

Ans :- 25 cups.

8. Winson gave $320 to his grandfather and 40% of the remainder to his mother. If 52% of his salary was given away and 10% of the salary was saved, how much did he save?

Ans :- He saved $160 .

9. The length and breadth of rectangle X are in the ratio 5:3. The length and breadth of rectangle Y are in the ratio 4:3. The perimeter of rectangle X and rectangle Y are in the ratio 4:7.
(a) Find the ratio of the area of rectangle X to the area of rectangle Y.
(b) If the area of rectangle Y is 33cm² bigger than the area of the rectangle X, find the area of rectangle X.

Ans :- a) 5 : 16
b) 15 cm².

10. In the sequence 2, 5, 8, 11…2 is the 1st term, 5 is 2nd term…Find the 100th term of this sequence. (2999)

Ans :- 2999.