P6 Math: Equal Quantity after 2 Parties undergo Fractional Decrease

The question presents 2 different items, each of different value and quantity.
After each undergo a fractional decrease, both items have the same number remaining.

The unit value of each item and the total value of the remaining items are provided.

Such questions require students to make use of "Equal Value Fractions" in order to solve.

These type of questions will usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Craig has a stack of $2 and $10 notes.

After using ²/₉ of the $2 notes and ³/₅ of the $10 notes to buy a figurine,

he has equal number of $2 and $10 notes remaining.

He has $672 left at the end.

How much money did Craig have at first? 

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P5P6 Math: Starting Difference Given with Both ending Equal at the End

This type of question begins with a value given(usually the difference between 2 parties).

Each of the value undergo fractional decrease and both ends up to be equal in the end.

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

Calculator usage is allowed.

Rachel has $105 more than Phoebe at first.

After Rachel spent ²/₃ of her money and Phoebe spent ¹/₄ of her money,

both girls have equal amount of money left.

How much did Rachel spend?

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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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P6 Math: Fractional Decrease of 2 different totals with 2 possibilities

This question type challenges the ability of students to handle fractions of 2 different totals.

Students need to be able to make use of the fractional decrease and the 2 values given (One of remaining total and one of difference between the 2 remaining values).

Such questions usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Jenny and Patsie have baked some cookies each.

If Jenny gave away ²/₅ of her cookies and Patsie gave away ¹/₂ of her cookies,

they will have 70 cookies left altogether.

But if Jenny gave away ²/₅ of her cookies and Patsie gave away ³/₄ of her cookies,

Jenny will have 19 more cookies than Patsie remaining at the end.

How many cookies did both girls bake altogether?

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P5/P6 Math: Before and After Fractional Decrease with Total at the End

2 values, in which one is a fraction of another, each undergoes fractional decrease and the total amount left is provided.

Such questions will need students to make use of common multiples and comparison models in order to solve.

Such questions are common in Paper 2 of P5/P6 exams.

Calculator usage is allowed.

An easier version of this question for P4 students can be found here.

Alan and Ben each have some water in their bottles.

The volume of water Alan have is ¹/₂ of the volume of water that Ben have.

After Alan drank ¹/₃ of his water and Ben drank ³/₄ of his water,

both boys have 560ml of water left altogether.

What is the total volume of water both boys have at first?

Army water bottle is also known as a water canteen

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P5/P6 Math: Starting Total Known with Both Parties undergoing Fractional Decrease

A total of 2 parties is given.

Each of the 2 parties undergo different fractional decrease.

The comparison between the amount left is given as multiple of another.

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

Calculator usage is allowed.

Similar questions of this type can also be found here.

Jayden and Keane have a total of $2024.

After Jayden spent ²/₅ of his money on a gaming console and

Keane spent ³/₄ of his money on a phone, 

Jayden has twice as much money left as Keane.

How much did Jayden have at first?

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P5/P6 Math: Starting Total and Ending Ratio (Basic)

The question type below provides the student with the starting total between 2 parties and the ending ratio after each of them undergo some changes. One of the value will undergo a fractional decrease and the other will have some value added or subtracted.

Students will need to "start from the end" in order to solve. (aka working backwards)

Such questions are common in Paper 2 of P5 and P6 papers.

Calculator usage is allowed.

Similar questions of this type can also be found here.

Moorthi and Devi have a total of 1093 invitation cards to send out.

After Moorthi sent out ¹/₃ of his cards and Devi sent out 444 cards of her cards,

the ratio of Moorthi's to Devi's remaining cards was 4:5.

a) How many cards did Moorthi sent out?

b) How many cards did they have left altogether at the end?

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P6 Math: Fraction of a Fraction of a Fraction

This questions splits up a total value into 2 groups.

After undergoing fractional decrease for each group, both are now of equal value.

Such questions are common on Paper 1 of P6 Prelim papers.

Calculator usage is not allowed.

There were some passengers in the airport waiting to board their planes.

²/₅ of the passengers were male and the rest were female.

After ¹/₄ of the male passengers and some female passengers boarded their planes,

there were equal number of male and female passengers whom have yet to board their planes.

What fraction of the female passengers have already boarded their planes?

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P5/P6 Math: Fractional Decrease of 2 parties of Equal Starting Ratio with Ending Difference Given

This question presents itself with 2 parties having equal ratio at first and both parties undergo difference fractional decrease. The difference at the end is also given.

Such questions are common in Paper 2 of P5 and P6 test/exam papers.

Calculator usage is allowed.

Pravin and Gary are postal delivery staff and 

have the equal number of packages to deliver in the morning.

By noon, Pravin has delivered ³/₄ of his packages and

Gary has delivered ⁶/₇ of his packages.

Pravin has 24 more undelivered packages than Gary.

How many packages did both have altogether in the morning at first?

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