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 3 confusing questions - Please Help!
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By: LimKopi (offline)  Friday, July 20 2012 @ 04:30 AM CDT (Read 1905 times)  
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1. 6 pupils took part in Maths competition. Their average score was 91. The max score each pupil could get was 100.
The 6 pupils had different scores and each score was a whole number. If one of the pupils scored 65 marks, what was
the minimum score the pupil in the third position could get?





2. A dog and a cat were having a chasing game with the dog chasing the cat.
Whenever the dog jumped once, it covered a distance of 1.8m.
Whenever the cat jumped once, it covered a distance of 1.1m.
The ratio of the number of times the dog jumped to the number of times the cat
jumped was 2 : 3. If the race started with the dog and the cat being 30 m apart,
how many meters must the dog jump before it could catch up with the cat?




3. A shopkeeper bought some mangoes to sell. On Monday, he sold them at
25% above the price he had paid and managed to sell 20% of the mangoes.
On Tuesday, he sold the mangoes at 13% less than the price he sold on Monday
and he managed to sell all the mangoes. He made a total of $ 900 from the sale
of all the mangoes in the 2 days. What was the price he had paid for the mango

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By: GIM (offline)  Friday, July 20 2012 @ 10:20 AM CDT  
GIM

Q1 solution:

Total score = 6 x 91 = 546
Since 1 person scored 65 marks, then total of remainding 5 person = 546 - 65 = 481

List down the possibilities starting with 100 as 1st number, then deduct each number from 481 to get the 5th person's scores.
481-100=381 ; 381-99=282 ; 282-98=184 ; 184-97=87

100--99--98--97--87 (the 3rd position is 98)
(1)--(2)--(3)--(4)--(5)

-99--98--97--96--91 (the 3rd position is 97)
(1)--(2)--(3)--(4)--(5)

-98--97--96--95--95 (not possible as the last 2 numbers are the same)

-97--96--95--94--99 (the 3rd position is 96)
(2)--(3)--(4)--(5)--(1)

-96--95--94--93--103 (not possible as the max is 100)

From the above, the minimum score for pupil in third position is 96.

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By: jo sarah (offline)  Monday, July 30 2012 @ 11:10 AM CDT  
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3. A shopkeeper bought some mangoes to sell. On Monday, he sold them at
25% above the price he had paid and managed to sell 20% of the mangoes.
On Tuesday, he sold the mangoes at 13% less than the price he sold on Monday
and he managed to sell all the mangoes. He made a total of $ 900 from the sale
of all the mangoes in the 2 days. What was the price he had paid for the mangoes?

Let the price paid for one mango be $p
and no. of mangoes be n. Thus, he paid $np for all the mangoes.

Monday: at $1.25p, sold 0.2n mangoes
so, he collected $1.25p x 0.2n = $0.25np

Tuesday: at $0.87 x 1.25p, sold 0.8n mangoes
thus, he collected $0.87np

In total, he collected $(0.25np + 0.87np) = $1.12np

He made (i.e profit) $1.12np - $np = $900
therefore, 0.12np = 900
and so, np = 900 / 0.12 = $7500

He paid $7500 for the mangoes.

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By: GIM (offline)  Friday, August 03 2012 @ 01:57 AM CDT  
GIM

Question 2

{---------------------? jumps------------------}
{---------30m---------}
|-------------------------|-------------------------|
Dog___________cat____________meet
Start__________start___________together

____Unit___Dist____ Dist units
Dog---2-------1.8m-------2 x 1.8 = 3.6
Cat----3-------1.1m-------3 x 1.1 = 3.3
Difference : 3.6 - 3.3 = 0.3 units

0.3 unit ----> 30m
1 unit-------> 30m / 0.3m = 100
Dog--------->2 x 100 x 1.8m = 360 m

The dog needs to jump 360m to catch up with cat.

Check :
(2 x 100 x 1.8) = (3 x 100 x 1.1) + 30m
________360 = 360

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