Q&A - PSLE Math

[tianzhu]

ooptimizer:

Thank you!

Hi

You're welcome.

Best wishes

[dnsy]

Appreciate anyone’s help on this question:


Mr lee left town M and travelled towards town N at an average speed of 80km/h. An hour later, mr Ong left town M and travelled towards town N at an average speed of 100km/h. Mr Ong passed town Q which was halfway between town M and town N 30 minutes earlier than mr Lee. If mr Ong reached town N at 10 pm , at what time did mr Lee leave town M for town N ?

Thanks!

[tianzhu]

dnsy:

Mr lee left town M and travelled towards town N at an average speed of 80km/h. An hour later, mr Ong left town M and travelled towards town N at an average speed of 100km/h. Mr Ong passed town Q which was halfway between town M and town N 30 minutes earlier than mr Lee. If mr Ong reached town N at 10 pm , at what time did mr Lee leave town M for town N ?

Hi

There are a few ways to go about this question.

For question on “Speed”, it helps to draw a simple diagram to show the relationships between two motorists on a timeline.

Using,the formula, Distance ------ Speed*Time with logical reasoning,

Head start by Mr Lee ------- 80km (1*80)

Time taken by Mr Ong to catch up with Mr Lee ------- 80/(100-80) ------- 4h

30mins -----1/2h
½ *80 -------40
40/20 ------ 2h (Mr Ong took another 2h to be 20km ahead of Mr Lee @midpoint.)

Mr Ong took a total of 6h to reach the midpoint.

Time taken by Mr Ong for the whole journey ------2*6 ------12h

Working backwards from 10pm,Mr Ong started his journey@10am

Hence, Mr Lee started @9am.

For students who are familiar with inverse proportion, here's an alternative.

From Town M ------ Town Q, Mr Ong took (1+0.5) or 1.5h less than Mr Lee.(half)
From Town M -------Town N, Mr Ong took (2*1.5) or 3h less than Mr Lee.(whole)

Speed Ratio
MrOng:Mr Lee ------ 100 :80 ------5:4

Time Ratio
MrOng:Mr Lee ------ 4:5

1 unit ----- 3h
Mr Ong ------4 units ------12h

Working backwards from 10pm,Mr Ong started his journey@10am

Hence, Mr Lee started @9am.

Best wishes

[Chan09]

Appreciate some help

A had a total of 2050 black and red marbles. He lost 3/5 of his black marbles and bought 150 red marbles. As a result the no. of red marbles he had was 1/4 of the remaining black. How many more black than red marbles he had at first?
Ans: 1950

[tianzhu]

Chan09:

Appreciate some help

A had a total of 2050 black and red marbles. He lost 3/5 of his black marbles and bought 150 red marbles. As a result the no. of red marbles he had was 1/4 of the remaining black. How many more black than red marbles he had at first?
Ans: 1950

Hi

This question was discussed in an earlier post.

Please refer to solution by MathIzzzFun.

Best wishes

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[stary]

Hi all,


Have a question to ask.

Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3:1. In the end, Azman and Bala had 780 and 480 marbles left respectively.

How many marbles did Azman have at first?

[MathIzzzFun]

stary:

Hi all,


Have a question to ask.

Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3:1. In the end, Azman and Bala had 780 and 480 marbles left respectively.

How many marbles did Azman have at first?

Hi

ratio -
Azman : Chongfu =125: 100 = 5:4
Chongfu : Bala = 160 : 100 = 8: 5
so, Azman : Chongfu : Bala = 10 : 8 : 5

Before losing the marbles,
Azman : Bala = 10 : 5 = 2u : 1u

Azman and Bala lost marbles in the ratio of 3:1 and had 780 and 480 left respectively.

Azman: Bala = 2u-780 : 1u-480 = 3:1
so 2u -780 = 3u - 1440, 1u = 660

at first, Azman had 2u = 2x660 = 1320 marbles.

cheers.

[TT2]

Hi I have another qn to ask…


In Jan, 80% of the members in a golf club were men. In jun, after 55 men had left and 75 women had joined the club, the % of the women increased to 40%. How many members were there in the golf club in Jan?

Thank you

[MathIzzzFun]

TT2:

Hi I have another qn to ask...


In Jan, 80% of the members in a golf club were men. In jun, after 55 men had left and 75 women had joined the club, the % of the women increased to 40%. How many members were there in the golf club in Jan?

Thank you

Hi

In Jan, ratio of men : women : 80:20 = 4u:1u ** total 5u
after 55 men left, and 75 women joined,
ratio of men : women
= 4u - 55 : 1u + 75
= 60 : 40
= 3 : 2

so, 8u - 110 = 3u + 225
5u = 335

Members in Jan = 5u = 335

cheers.

[stary]

Thanks MathIzzzFun for your prompt reply!