Solving ratio problem sums involving overlapping figures is an essential skill for students in P5 and P6 exams. It is a common way for schools to test students’ understanding of ratios and proportions. To help students master this skill, this video will provide a simple step-by-step guide to help them understand the mechanics of solving ratio problem sums involving overlapping figures.

RATIO, GROUP UNCHANGED

Yenni has 25% more stamps than John. If Yenni loses 676 stamps, she will have 1/6 as many stamps as John. How many stamps do they have altogether?

RATIO, DIFFERENCE UNCHANGED

The ratio of the amount of money John had to the amount of money Peter had was 4 : 7. After each of them spent $28, the ratio became 3 : 7. Find the amount of money John has now.

RATIO, TOTAL UNCHANGED WITH SCENARIOS

John and Peter had some apples. If John gives away 12 apples, the number of apples John had to the number of apples Peter has will be 3 : 5. If Peter gives away 12 apples, John will have 3 times as many apples as Peter. How many apples did they have altogether?

RATIO, ALL CHANGED (UNITES AND PARTS)

In a class library, the number of fiction and non-fiction books is in the ratio of 5 : 1. If we remove 4 fiction books and add 2 non-fiction books from the library, 1/5 of the books will be non-fiction books. How many books are there in the class library?

RATIOS PROBLEM SUMS INVOLVING PROPORTION TRANSFER

PROPORTION EXTERNAL TRANSFER

Peter and John had $510 altogether. Peter gave 40% of his money to his father and John spent 75% of his money. They then had an equal amount of money left. How much money did Peter give to his father?

PROPORTION AND QUANTITY EXTERNAL TRANSFER

There were 240 apples and pears in a box. John removed 4/7 of the apples from the box and added 30 pears into the box. As a result, there was an equal number of apples and pears in the box. How many apples were there in the box at first?

PROPORTION EXTERNAL TRANSFER ALL GROUPS CHANGED

A total of 20 boys and girls attended a performance in the school hall. 3/4 of the boys and half of the girls left the hall after the performance ended. There were 7 children remaining in the hall. How many girls were there at first?

PROPORTION EXTERNAL TRANSFER, BEGIN WITH DIFFERENCE

Box A had 48 kg more rice than Box B at first. After John used 1/3 of the rice in Box A and 1/4 of the rice in Box B, Box A had 17 kg more rice than Box B. How much rice was there in Box A at first?

PROPORTION INTERNAL TRANSFER

John and Peter have 240 cards altogether. If Peter gives 1/9 of the cards to John and John in turn gives 1/4 of his cards to Peter, they will have the same number of cards. How many cards does Peter have?

PROPORTION INTERNAL TRANSFER, BEGIN WITH DIFFERENCE

Yenni and John shared some sweets. Yenni had 80 more sweets than John. After Yenni gave 20% of her sweets to John, John had 20 more sweets than Yenni. How many sweets did Yenni give to John?

PERCENTAGE

PERCENTAGE INVOLVING DISCOUNT AND GST

John wants to buy some boxes of mangoes for $160. A discount of 20% is given to him on the mangoes. As a result, John is able to buy 8 more such boxes of mangoes with exactly $160. What is the price of one box of mangoes before the discount?

PERCENTAGE INVOLVING CHANGE

Peter saves 30% of his monthly salary. When his salary increased by 10%, his savings increased by $189. Find Peter’s salary before the increase.

PERCENTAGE DISCOUNT

John bought a pair of shoes for $153 after a discount of 15%. a) What is the usual price of the pair of shoes before discount? b) He bought a bag at $48 at the same shop. The total discount for both the pair of shoes and the bag was $39. What was the percentage discount given for the bag?

GEOMETRY AND ANGLES

ANGLES APPLICATIONS

ANGLES APPLICATIONS

ANGLES APPLICATIONS

CIRCLES

CIRCLE APPLICATION AREA OF PETAL

CIRCUMFERENCE OF CIRCLE APPLICATION

CIRCLES

The figure below is made up of a big square, a small square and a circle. The ratio of the area of the big square to the area of the circle is 14 : 11. What fraction of the figure was shaded? Give your answer in its simplest form?

SPEED

SPEED INVOLVING COMPARISON OF QUANTITY

Peter and Amber started walking from the same place but in opposite directions along a straight road. After walking for 3 hours, they were 8 km apart. Amber’s average walking speed was 1 km/h less than Peter’s. Find the distance that Peter covered.

TRIANGLES, AREA AND PERIMETER

AREA AND PERIMETER

The figure below, not drawn to scale is formed by 4 identical right-angled isosceles triangles and a square in the centre. The shaded area of the figure is 200cm². Find the perimeter of the square.

AREA OF TRIANGLES INVOLVING COMMON HEIGHT

In the figure below, not drawn to scale, ABCD is a trapezium. Given that AB is parallel to DC and area of triangle ABD is 54 cm², find the area of triangle BCD.

CHALLENGING PROBLEM SUMS

PATTERN

1 cm square tiles and triangular tiles were used to make some figures. The area of each triangular tile was half that of a square tile. The first four figures are shown below.

CHALLENGING QUESTION

Ali, Ben, Charles and Dave had some stickers. Ali and Ben had a total of 17 stickers. Ben and Charles had 16 stickers in all. The product of the number of Ali’s stickers and the number of Charles’s stickers was 30. Given that Ali had 2/3 as many stickers as Dave, How many stickers did the children have altogether?

PATTERN

A trapezium-shaped table can seat 5 people (as shown in Figure 1). Amber uses the trapezium-shaped tables to form figures that follow a pattern to plan the number of people sitting around the tables for a gathering. The first three figures are shown below.

VOLUME AND RATE

An empty rectangular pool measures 44 m by 20 m by 2 m. Pipes A and B are filling the pool at rates of 32 m³/min and 40 m³/min respectively. Pipe A was turned on first. Pipe B was turned on 10 minutes later. If Pipe A was turned on at 9 a.m., what time would the tank be completely filled with water?

DIFFERENCE REDISTRIBUTION

Amber prepared some dough for baking. She divided the dough into equal portions, each weighing 25 g. If she had divided the dough into 20-gram portions instead, she would have 9 more portions of dough. What is the total amount of dough that Amber prepared? Express your answer in kg.

DIFFERENCE REDISTRIBUTION

John has $60 and Peter has $11 in their respective bank accounts. Every day, John deposits $7 while Peter deposits $14. In how many days will Peter have $21 more than John?