P5P6 Math: Value and Multiples and Differences

This is a question type that will provide 4 of the listed information below for 2 different items of different quantities,

1. Total value of 2 items
   
   
2. Difference between 2 item's totals
   
   
3. Unit Difference between 2 items
   
   
4. Multiples of 1 item compared with another 

Similar questions using ratio to represent the multiples can also be found here and here.

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

Calculator usage is allowed

Samy bought thrice as many books as pens.

He spent a total of $3850 on all the books and pens.

Each book cost $5 more than each pen.

He paid $2030 more for all the books than for all the pens.

How many books did Samy buy?

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P5/P6 Math: 3 Item Types with Different Quantities and Values

Such questions uses fraction and multiples(ratio) to give a breakdown of the distribution of 3 different items. Each of the item have different values and the total value of all quantities of 3 items is also provided.

Such questions are common in Paper 2 of P5 exams.

Calculator usage is allowed.

Erica bought a number of durians,watermelons and jackfruits 

from the market and spent $620 altogether.

¹/₂ of all the fruits bought were durians.

The ratio of the number of watermelons to jackfruits bought was 3:2.

Each durian costs $20, each watermelon $4 and each jackfruit was $6.

How many durians did Erica buy?

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P5/P6 Math: Different Multiples of 2 Items with Same Total Value (Individual Difference Given)

2 items of different quantities have the same total value.

The difference between each item is also given.

Such questions can appear in both P5 and P6 Paper 2.

Calculator usage is allowed.

3 bottles of soy sauce cost as much as 5 bottles of cooking oil.

A bottle of soy sauce costs $17.60 more than each bottle of cooking oil.

Find the cost of one bottle of soy sauce.

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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 Math: Set Method (Total Given)

Set method, often confused with assumption, because the total value is given.

Students need to differentiate between the 2 by noticing that the total quantities of both items were not given, hence not able to "assume".

Such "Set" questions often appear in Paper 2 of P5 exam papers.

Calculator usage is allowed.

More of such P5 set questions here.

Greg bought 5 times as many toy cars as toy trucks.

Each toy car costs $2 and each toy truck costs $5.

He spent a total of $120 of all the toy cars and toy trucks.

How many toy cars did Greg buy?

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P6 Math: Quantity and Value Difference and Ratio

The question type below provides the numerical quantity of 2 different items.
Each item has its own unique unit value but only the difference between each item's unit value is given.
The ratio of the total value between 2 items is also provided.

Such questions usually appear in Paper 2 of P6 Prelims or Mid-year papers.
Calculator usage is allowed.

Alison has 14 small tables and 3 big tables in her restaurant.

Each big table can seat 4 more diners than each small table when fully occupied.

On nights when all the seats are occupied, ⁷/₉ of the diners are seated at the small tables.

How many diners can be seated in each big table?

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P6 Math: Same total quantity of 2 different items of different values

This question type is made famous during the 2021's Math PSLE exams.

The "Helen and Ivan" question.

2 items of different quantities and value are split into 2 groups containing same number of items. The individual value difference a between 2 items and the total value of one of the group [ containing different quantities of 2 items ] are given.

This is a P6 PSLE Paper 2 question.
Calculator usage is allowed.

Helen bought 64 pencils and some notepads.

Ivan bought 104 pencils and some notepads.

Both Helen and Ivan bought the same total number of notepads and pencils.

Each notepad costs $2.70 more than each pencil.

Helen spent a total of $1134 on their pencils and notepads.

How much did Ivan spend on all his pencils and notepads?

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P3/P4 Math: Two Fractions of Total Given

Fraction problem sums are common in Section C of P3 and P4 exams.

A "fraction of the total" representing one item and another "fraction of the total" representing another item. 

The third information given is usually the value of the first item, second item or the amount left.

A slightly more complex version of this question can be found here.

Bala have some books.

¹/₃ of his books are about cars.

¹/₉ of the books are about planes.

The rest of the books are about dinosaurs.

He has 55 books about dinosaurs.

How many books does Bala have altogether?

A Stegosaurus from the Jurassic Period

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P5/P6 Math: Revisiting Value and Ratio Differences

This question is a variation of a tough P5/P6 Paper 2 high value question.
(A slightly more complex version of this question can be found here. )

2 different item of different quantities and individual values.

Only 4 information/numbers are given,

Namely

1) Total value of both items

2) Ratio between the quantity of both items

3) Individual value difference between both items

4) Total value difference between both items

Calculator usage is allowed. 

Tom has marbles placed in blue and red boxes.

The number of blue to red boxes is in the ratio of 7:6 respectively.

Each blue box contains 6 less marbles than a red box.

There are a total of 3834 marbles in both type of boxes.

The number of marbles in all the red boxes is 54 more than

all the marbles in the blue boxes.

How many marbles are there in each red box?

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P6 Math: Difference between 2 total values of different quantities

The question type below deals with 2 different items, each with different individual values and quantity. The difference in terms of the total value between the 2 items are given.

Such questions often appear in P6 mid year exam onwards.

This is a paper 2 question so calculator is allowed

A simpler version of this question for P5 students can be found here.

Catherine has a piggy bank
containing only 20-cent coins and 50-cent coins.

She has 7 more 50-cent coins than 20-cent coins in the piggy bank.
The total value of the 50-cent coins is $7.40 more than the total value of all her 20-cent coins.
How many 20-cent coins does she have in the piggy bank?

What is the mass of each different denomination of coins in Singapore?

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P6 Math: Fractions : Buying 2 different items of different quantity and different value

The question type below deals with buying 2 different items of different values and different quantity.
Such questions often appear in P6 mid year and P6 Prelim paper 2.
Calculator use is allowed

Greg spent ³/₄ of his money on 3 spoons and 6 forks.

Each spoon cost thrice as much as each fork.

He spent all his remaining money on buying more forks.

How many forks did Greg buy altogether?

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P5/P6 Math: Value and Ratio and Differences

This is a common P5 SA2 and P6 Math question that is usually worth 4 marks or more.

Such questions will appear in Paper 2.

Calculator usage is allowed.

(An easier version of this question can be found here)

Rick spent a total of $31.20 buying some erasers and pens.

The ratio of pens to erasers was 9:2.

The total value of all the pens is $26.40 more than the total value of all the erasers.

Each pen costs $0.50 more than an eraser.

a) How much is an eraser?

b) How many pens did Rick buy?

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