P5P6 Math: Percentage Decrease of One Value vs Percentage Decrease of the Total

While percentage simply means a fraction of 100, the concept of percentage becomes complex when the terms such as percentage increase or decrease is in play.

Such questions usually appear in P5 and P6 exams in Paper 2.

Calculator usage is allowed.

In June, Alan was given an allowance of $200.

Alan spent 20% of his allowance on food and 30% of the allowance on transport.

He saved the remaining of the allowance in June.

In July, he was given less allowance.

So he spent 20% lesser on food but spent the same amount on transport and saved the same amount as in June.

What was the percentage decrease of his allowance in July?

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P6 Math: 3 Parties Before and After with Uneven Ratio at the End

A total of 3 parties are given at first.
Each of the party undergo increase or decrease and the end ratio is given.

Some of the increase/decrease are fractional and some are numerical.

Such questions are common in Paper 2 of P6 exams

Calculator usage is allowed.

An easier version of this question can be found here.

Elizabeth, Wendy and Lindy had a total of $483 at first.

Elizabeth was given more money by her parents and had double of what she had at first.

Wendy spent $67 on a pair of ballet shoes and Lindy's brother gave her another $94.

In the end, the ratio of remaining money of Elizabeth to Wendy to Lindy was 5:4:2.

How much did Lindy have at first?

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P5/P6 Math: Before and After with Percentage and Fractional Decrease

This question type begins with the total of 2 values given at first.

One of the value undergo percentage decrease and the other a fractional decrease.

Both values become equal at the end.

Students will need to work backwards in order to solve such questions.

These questions are common in Paper 2 of P5 and P6 exams.

Calculator usage is allowed.

Mr Tan and Mr Lee had a total of $418 at first.

After Mr Tan spent 75% of his money on a gift and Mr Lee spent ¹/₃ of his money on lunch, both men had equal amount of money remaining.

How much did each have remaining at the end?

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P5/P6 Math : 3 Parties Before and After with Equal Amounts at the End

This Before and After problem sum starts with the total of 3 parties given.

Each party undergo either numerical increase, numerical decrease and/or fractional decrease. The problem sum ends with each party having equal ratio in the end.

Such questions are common in P5 and P6 Paper 2.

Calculator usage is allowed.

Ben, Carl and Dave have a total of 1021 marbles at first.

After Ben halved his number of marbles by giving some away, 

Carl bought 118 more marbles and Dave threw away ¹/₅ of his marbles,

each boy have the same number of marbles left.

How many marbles did Dave have at first?

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P5 Math: Uneven Ratio becomes Equal after Both Decrease

This question provides the ratio of 2 items at first.
After both undergo different decrease in value, both ends up being equal with one another.

Such questions are common in WA2(mid year) for P5.

Calculator usage may be allowed.

A similar but "inverted" version of this question can also be found "here".

Alan and Rick each have pencils in the ratio of 5:8.

After Alan gave away 32 pencils and Rick sold 77 pencils.

They have equal number of pencils remaining.

How many pencils did Rick have at the end?

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P6 Math: Before and After Percentage Decrease with Value Increase

This "Before and After" question provides the total before and the total after the change.

One of the party undergo percentage decrease while the other party undergo a value increase.

Such questions are common in Paper 2.

Calculator usage is allowed.

At first, there were 180 adults and children in a cinema.

After an additional 24 adults entered the cinema and 25% of the children went home,

there were a total of 179 adults and children in the cinema at the end.

How many adults were there at the end?

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P5/P6 Math: Before and After ( Starting Difference with Ending Ratio)

Such questions are common for P5 and P6 exams.

Where the starting difference is known and the ending ratio is given after some numerical increase/decrease is applied to both parties.

As these appear mostly in Paper 2,

calculator usage is allowed.

A similar "before and after" type question can also be found here.

Eric has 450 more items listed on his online store than Kelvin.

After Eric sold 45 items and Kelvin listed 3 more items for sale,

the ratio of Eric's items for sale to Kelvin's items for sale became 3:2.

How many items did both have listed for sale at first?

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P5/P6 Math: Starting Ratio and Ending Fraction of Total Given

This question type starts with the ratio of 2 parties given.

One of them undergo fractional decrease and the other one has a numeral decrease.

The remaining, which is a fraction of the total, will also be provided.

Such questions will appear in P5 SA2 and P6 exams Paper 2.
Calculator usage is allowed.

The ratio of money that Charles and David have are in the ratio of 4:5 respectively.
After Charles spent ¹/₂ of his money on lunch and David spent $28 on a taxi ride,
the total amount they have left is ¹/₃ of the total amount they had at first.

How much money did both have left at the end altogether?

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P6 Math: One Party Reduced to Zero with Starting Difference Given

The following question deals with "constant decrease".
The starting difference between 2 parties is known and both parties undergo constant decrease.

One party will be reduced to zero while the other will have some left.

Such questions usually appear in Paper 2.
Calculator usage is allowed.

Shane have 40 more flyers than Derek at first.

Every minute, Shane gave out 18 flyers and Derek gave out 15 flyers.

When Shane has given away all his flyers, Derek still has 35 flyers remaining.

How many flyers do they have altogether at first?

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Students may find these question types to be similar.

P5/P6 Math: Fraction of Remaining (Intermediate)

The following question type require students to be able to understand "fraction of remaining".

2 fractions are given to represent 2 items
and 2 numbers are given to represent one of the items and the final amount left.

Such questions appear in P5 and P6 exams and will be in Paper 2.
Calculator usage is allowed.

Joe started reading a novel.

He read ²/₅ of the novel on Monday.
He read another 58 pages of the novel on Tuesday.
After reading ¹/₄ of the remaining novel on Wednesday,
he finished reading the last 96 pages of the novel on Thursday.

How many pages were there in this novel?

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P5 Math: Lesser Number of Shares Increasing Cost of Each Share

The question type below deals with equal share with total unchanged.
But each share increases due to lesser number of people sharing the total.

P5 SA2 type question for Paper 1.

No calculator allowed.

5 girls shared to buy Alvin a watch for Christmas. One of the girls calculated wrongly and divided the cost of the watch by 6. Because of that, each girl's share became $8 lesser. How much was this watch?

How do automatic watches work?

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P6 Math: One Party Reduced to Zero with Starting Ratio Given

The question type below deals with 2 parties with different ratios given at the start.
Each will have different amount deducted every instance until one party reaches zero.

Such questions often appear in P6 paper 2 during SA1 and prelim.

Calculator is allowed.

Geraldine has red and blue pins in the ratio of 3:4 respectively.

For every 5 red pins she used, 3 blue pins will also be used.

After all the red pins were used, there were 132 blue pins remaining.

How many red and blue pins did Geraldine have altogether at first?

20 of the most visited countries in the world

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P5/P6 Math: Fraction of Remaining (Advanced)

The question type below deals with "fraction of remainder" (with a twist).
The first fraction is not a fraction of total but a fraction of remainder.

Such questions often appear in Paper 2 starting from P5 mid year exam onwards .

Calculator usage is allowed.

In a basket containing red, green and blue beads,

56 beads were red.

¹/₃ of the remaining beads were green.

The blue beads make up ¹/₅ of all the beads in the basket.
How many beads were there altogether?

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