Four Primary 6 Maths problem sums from our Term 1, Week 4 worksheet. Explore fractions and ratio with a hint when you need it, and a clear worked solution when you’re ready.
A train left Punggol Station with some passengers. At Seng Kang Station, no passenger alighted and the number of passengers who boarded the train was 1/5 of the original number of passengers on the train. At Buangkok Station, 36 passengers alighted and 80 passengers boarded the train. At Kovan Station, 40 passengers alighted and thrice as many passengers boarded the train. In the end, there were 820 passengers left on the train. How many passengers were there on the train initially when it left Punggol Station?
Show a hint
Undo the changes at Kovan and Buangkok first. Then compare the passengers after Seng Kang with the original number.
Remember: When working backwards, reverse each operation: boarding becomes subtraction and alighting becomes addition.
P6 Maths · Term 1 Week 4 · Section C, original question 1
02
A day at the funfair
The ratio of the number of children to the number of adults at a funfair was 6 : 7. Of the children who attended the funfair, 3/5 were boys. There were 51 more adults than boys. How many people were at the funfair?
Show a hint
Scale 6 : 7 so the children have a multiple of 5 units. You can then find the boys without fractional units.
Find the boys and the differenceBoys = 3/5 × 30 = 18 units. Adults − boys = 35 − 18 = 17 units.
Find one unit17 units = 51 people. 1 unit = 51 ÷ 17 = 3 people.
AnswerTotal = (30 + 35) × 3 = 195 people.
Check your answer: Children = 90, adults = 105, boys = 54. Then 90 : 105 = 6 : 7 and 105 − 54 = 51.
Remember: The 51-person difference compares adults with boys, not adults with all the children.
P6 Maths · Term 1 Week 4 · Section C, original question 3
03
Red and blue marbles
In a box, there were some red and blue marbles. At first, the number of red marbles was 3/7 of the number of blue marbles. After 12 red marbles were taken out and 12 blue marbles were put into the box, the ratio of the number of red marbles to the number of blue marbles became 1 : 4. How many marbles were there in the box?
Show a hint
The number removed equals the number added, so the total stays the same. Express both ratios with the same total number of units.
Show worked solution
Keep the total constant
Red at first: 3 of 10 units
Red at the end: 2 of 10 units
The total stays at 10 units. Red decreases by 1 unit, which represents 12 marbles.
Compare equal totalsAt first, red : blue = 3 : 7, a total of 10 units. At the end, 1 : 4 = 2 : 8, also 10 units.
Find the change in red marblesRed marbles decreased from 3 units to 2 units. The decrease of 1 unit represents 12 marbles.
AnswerTotal = 10 × 12 = 120 marbles.
Check your answer: Initially red = 36 and blue = 84. Finally red = 24 and blue = 96. Then 24 : 96 = 1 : 4; the total remains 120.
Remember: Equal totals let us use the same-sized units before and after the change.
P6 Maths · Term 1 Week 4 · Section C, original question 4
04
The stamp collection
The ratio of the number of foreign stamps to local stamps in a stamp album is 9 : 7. There are 245 local stamps, and the rest are India and Malaysia stamps. The ratio of the number of India stamps to the number of Malaysia stamps is 2 : 3. After some Malaysia stamps are removed, the number of Malaysia stamps is 2/5 of the number of local stamps. Find the number of Malaysia stamps removed.
Show a hint
First find the foreign stamps, then the Malaysia stamps. The number of local stamps does not change.
Show worked solution
Find each part in turn
Malaysia stamps at first: 189
Malaysia stamps remaining: 98
Compare the lengths using the same-sized units.
Find all foreign stamps7 units = 245 local stamps. 1 unit = 35, so foreign stamps = 9 × 35 = 315.
Find Malaysia stamps at firstIndia : Malaysia = 2 : 3. Malaysia stamps = 3/5 × 315 = 189.
Find Malaysia stamps remainingLocal stamps remain 245. Malaysia stamps remaining = 2/5 × 245 = 98.
AnswerMalaysia stamps removed = 189 − 98 = 91.
Check your answer: India = 126 and Malaysia = 189, giving 2 : 3. After removing 91, Malaysia = 98 = 2/5 × 245.
Remember: In 3/5, the whole is the foreign stamps. In 2/5, the whole is the local stamps. They are different wholes.
P6 Maths · Term 1 Week 4 · Section C, original question 5
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