P4/P5 Math: Starting Multiples and Ending Multiples After Equal Decrease in Value

"Before and After Comparison Models" are staple for P3 to P6 Math.

The folowing question type presents one party to be a multiple of another at first.

After both undergo an equal decrease in value, the ending comparison is another multiple of one another.

Such questions are common in P4 Section C and P5 Paper 1.

Calculator usage is not allowed.

Kenneth has thrice as many baseball caps as Hiroshi at first.

After each gave away 45 caps,
Kenneth still has 8 times as many baseball caps as Hiroshi.

How many caps did both have altogether 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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P5/P6 Math: Exchange until One Party becomes Zero

This question type requires students to work backwards to derive the initial number of both items at first.

A total of 2 different items are presented at first.

One of the items will be replaced with a multiple of the other item.

This is repeated until all of the items are now the same type.

Such questions are common in Paper 1 of P5 and P6 exam papers.

Calculator usage is not allowed.

Danielle has a total of 48 erasers and pens.

After trading each of her pen for 5 erasers,

she now has a total of 72 erasers after trading all her pens.

How many pens does she have at first?

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P6 Math: Average of 3 different numbers

With the average of a certain number of values, it is possible to find their total.

With a known value of two of the numbers, it is possible mathematically to find the third value of the group of 3.

This question type requires first for students to be able to find the total before using logic to deduce and calculate the largest possible value of the 3 numbers.
( while complying with the rules of all being different numbers,etc etc )

Such questions are common in Paper 1 of P6 exams.

Calculator usage is not allowed

The average of 3 different two digit numbers is 29.

What could be the value of the largest possible number?

(FYI, the answer is neither 29 nor 99)

Jim Carrey as the Riddler in Batman Forever (1995 movie)

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P6 Math: Fractions with Different Values

Such "fraction" questions are further complicated by having different values tagged to each group. Each of the "fraction of total" and "fraction of remaining" and "left" groups have different values/scores/points.

These questions often appear in Paper 2.

Calculator usage is allowed.

During a carnival, a total of 1748 play tokens were given out free to children whom visited.

¹/₄ of the children received 5 tokens each and 

²/₅ of the remaining children received 4 tokens each.

The rest of the children each received 3 tokens.

How many children visited the carnival?

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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?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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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?

If the above question is easy, try to do the more challenging question below.

The question below will randomize with different numbers every hour. 

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