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 By: Kuro (offline)  Wednesday, May 22 2013 @ 08:20 AM CDT (Read 1353 times)
Kuro

Could someone help solve the questions below?

Q1. At a carnival, there were 40% more males than females. There was an equal number of males without caps to the number of females without caps. The number of males with caps to the number of females with caps was 6 : 2.
(a) What was the ratio of the number of females with caps to the number of females without caps?
(b) Midway, 800 females with caps left the carnival. In the end, there were 3/7 as many females as males remaining behind. How many people were at the carnival first?

Q2. Faris had some stickers. He gave 1/5 of his stickers to his sister and 1/8 of the remainder to his brother. After buying another 96 sticker, Faris had 9/10 of the stickers that he had at first. How many stickers did Faris have at first?

Q3. Town A and Town B were 684 km apart. After 10.45, Jack drove from Town A to Town B. At the same time, Roy drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Roy and Jack passed each other at 15.30. If Jack was travelling 18 km/h slower than Roy, find Roy's speed.

Junior

Registered: 12/31/06
Posts: 27

 By: echeewh (offline)  Wednesday, May 22 2013 @ 04:52 PM CDT
echeewh

Hi <Kuro>,

It will be much appreciated if you can provide the <answerkey> at the same time to verify in future. Thank you.

Following pls find my worked solution for Q2 , 3:

Q2.

*** - for alignment purpose

<------------------ Total ------------------->
|----|----|----|----|----|----|----|----|----|----|-------|
<- S --><B> ************************* < 96 >
*********** <------------- (9/10) total ---------->

2u --> 96
1u --> 48

Total (at first) = 10u --> 10 × 48 = 480

=========

Q3.

<------------------- 684 km ----------------->
|-------------------------------------------------|
A ************************************* B
|-> ************* |-> ***************** <-|
J ************** J1 ******************* R
Sj=(Sr-18) ** <-| ********************* Sr
t=1045 ******* R1 ****************** t=1045
************* t1=1530

t(JJ1) = t(RR1) = 1530 - 1045 = 4 h 45 min = 4 3/4 h

Time taken (meetup) = 684 ÷ [(Sr - 18) + Sr]
19/4 = 684 ÷ (2Sr - 18)
2Sr - 18 = 684 ÷ (19/4) = 684 × (4/19) = 144
2Sr = 144 + 18 = 162
Sr = 162 ÷ 2 = 81

Roy's speed = 81 km/h

==========

Trust this helps.

Do let me know again if this is different from your <answerkey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: puahkh (offline)  Tuesday, May 28 2013 @ 04:48 AM CDT
puahkh

Male 140%
Female 100%

Mc:Fc
6:2

Mw:Fw
1:1
8:8 (Guess and Check method)

Mc+Mw = 14
Fc:Fw = 10

Fc: Fw

M: F
14:10
7:5 (12 U)

2U =>800 female
1U => 400
12U => 4800 (answer to (b))

Newbie

Registered: 05/27/13
Posts: 1

 By: echeewh (offline)  Tuesday, May 28 2013 @ 03:11 PM CDT
echeewh

Hey All,

Further to <puahkh> answer to Q1, I 'm still doubting the clarity of the question for (b) while agreeing with (a). Thats why I held back my response to this while releasing the other two worked solutions.

By the way, the ratio of females with caps to females without caps is 1 : 4. ( <puahkh> 's ratio is not simplified ).

In addition, the ratio of males without caps to females without caps is 8 : 8 , which is by no means, Guess and Check. Here's how ...

<before>
M : F
140 : 100
14 : 10

F - M = 4u

Mnc : Fnc
1 : 1

Mc : Fc
6 : 2

Given that there's an equal number of Males and Females (without caps) {Mnc = Fnc}, the difference of 4 units(u) between Males and Females {F - M = 4u} comes from the difference between Males and Females (with caps) {Mc - Fc = 4u}.

Since M : F is 14 : 10,
Mnc = 14u - Mc = 14u - 6u = 8u
Fnc = 10u - Fc = 10u - 2u = 8u

Mnc : Fnc
8 : 8

Next, the clarity of the question for (b) lies in this statement " ... 800 females with caps left the carnival ... ".

Using <puahkh>'s answer of 4800, there would be 2800 Males and 2000 Females {24u --> 4800; 1u --> 200}. At first, there were ..

Mc : Fc
6 : 2

Fc (females with caps) = 2u --> 2 × 200 = 400

So my doubt is how can 800 females with caps left the carnival when there were only 400 at first ???

<puahkh>'s answer of 4800 would be correct if the statement is rephrased as " ... 800 females left the carnival ... ".

=======

Trust this clarifies.

Best regards,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: Kuro (offline)  Sunday, June 02 2013 @ 08:30 PM CDT
Kuro

Thanks you guys for the help.

Junior

Registered: 12/31/06
Posts: 27

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