Name : ____________________    Date   : _____________

                                                          Score : _____________

Write down your correct answer and show your workings:

  1)  At a party, Sarah distributed 18 sweets to each of the boys and 20 sweets to each of the girls and had 48 sweets left. 
       If she had distributed 20 sweets to each of the boys and 18 sweets to each of the girls instead, she would have 32 sweets left. 
       If Sarah had 40 pupils in her class,
       a) How many more boys than girls were there in her class? 
       b) How many sweets did she have at first?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

  2)  There were 2 identica flights of steps. For the first flights of steps, Siti walked up some steps adn ran 4 steps and 
        took a total of 75 seconds. For the second flight of steps, she walked up some steps and ran 11 steps and took a total 
        of 40 seconds. How long will Siti take if she had walked up both flight of steps? Leave your answer in seconds.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

  3) May earned twice as much money as her brother. After May spent $32 and her brother spent $50, the ratio of money 
      May had left to the amount of money her brother had left was 7:3. 
      Find the amount of money May earned.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

  4)  The club has 1150 members. 20% of men and 25% of women are non professional photographers. 
       A total of 250 members are non professional photographers. 
       How many more men than women are there in the club?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

  5) Bobby, Edward and kelvin made a bottle of paper stars. 
     The number of paper stars Bobby made was 21 more than 1/4 the total number of paper stars in the bottle. 
     The number of paper stars Edward made was 30 more than 1/4 of the remaining number of paper stars in the bottle. 
     Kelvin made the remaining 114 paper stars. 
     How many paper stars did they make in all?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Answers:

  1) 
Scenario 1: 

Boys : 18 sweets each 
Girls : 18 sweets + 2 sweets each 
Left : 48 sweets 

Scenario 2 : 
Boys : 18 sweets + 2 sweets each 
Girls : 18 sweets each 
Left : 32 

So, no. of sets of 18 sweets will be the same in both scenarios. 
The only difference is the sets of "2 sweets". 

Difference in sets of 2 sweets = 48 - 32 = 16 
16 = 8 sets of 2 sweets 

(a) There are 8 more boys than girls. 

(b) Total no. of pupils = 40 
no. of girls = 16 
no. of boys = 24 
no. of sweets = (18 * 24) + (20*16) + 48 = 800

  2) 
Assuming Siti walked and ran at the same constant speeds: 

Time difference in running up (11-4) 7 steps = 75-40 = 35s 
So additional time taken to walk up 1 step = 35/7 = 5s 
Additional time taken to walk up 4 steps = 4x5 = 20s 

Total time taken to walk up 2 flights of steps 
= 2 x (20+75) = 190 
or = 2 x (11x5 + 40) = 190

  3)
May ____________________________ ____________________________ 

May {---------32-------}{----------------------7 units-----------------------------------}

Bro ____________________________ 

Bro {------50-------------}{----3units----} 

So the equation is: 

32 + 7 units = 2(50 + 3 units) 
32 + 7 units = 100 + 6 units 
1 unit = 100-32 = 68 

Hence May earned 7(68 )+32 = $508

  4) 
This question is changing % into fractions as it is easier to think in 1 unit than as 20% or 25%.
20% = 1 in 5 parts 
25% = 1 in 4 parts 

it is known total people = 1150 
total non-photographers = 250 
20% men and 25% women = 250 so in fraction: 
1 unit of men + 1 unit of women = 250 

since 1 unit of men and 1 unit of women are different things, it is hard to make comparison, however, we know that if we take away 4 units from men and women, the remainder is 1 unit of men.

hence 250*4 = 1000 
1150-1000 = 150 
Only then you will know 1 unit of men(=20% of men) = 150 

so total men(100% of men) = 150*5 = 750 

1 unit of women(=25% of women) = 250-150 = 100 

so total women (100% of women) = 100*4 = 400 

hence difference between men and women = 750-400=350

  5) 
Start backwards from Edward. Since Edward made 30 more than a quarter of the stars and Kelvin made the rest, it means that Kelvin's stars plus 30 makes up 3/4 of the stars,
ie. 114 + 30 = 144 is 3/4 of the stars
So the sum of Edward's and Kelvin's stars is 144 x 4/3 = 192

We apply the same principle with Bobby's stars now.
3/4 of the total stars = 192 + 21 = 213
So the total number of stars made by all 3 children is 213 x 4/3 = 284

(A+B+C)/3 = (A+B)/2 + 5 
A+B+C = 3(A+B)/2 + 15 
A+B+38 = 3(A+B)/2 + 15 
A+B+23 = 3(A+B)/2 
2(A+B)+46 = 3(A+B) 
=> A+B = 46 
=> A+B+C = 46 + 38 = 84

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