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Question

Hi,

Need help with this. Somehow…. I can’t think already…. mental block. 🙁

Thanks in advance.

 

Tank X and Tank Y contain some water. If 46.5 litre of water is drained from Tank X, the volume of the water in Tank X will be 3/8 of the total amount of water in Tank X and Tank Y. If 35.2 litre of water is drained out from Tank Y, the volume of the water in Tank Y will be 15% less than that of the water in Tank X. What is the total volume of water in Tank X and Tank Y ?

Answer

Hi,

This is a rare question.

Its feature is  “if … if”.

It appear since Primary 3. Something like if A give 10 to B, they will be equal. If B give 10 to A, they will be in certain ratio. 

It includes After – Before and  Before – After scenario. 

 

We shall start from the first if.   

If 46.5 litre of water is drained from Tank X, the volume of the water in Tank X will be 3/8 of the total amount of water in Tank X and Tank Y.

This means that at After X : Y = 3 : 5.

We shall reverse the pouring to Before.

  Tank X            Tank Y          Total    
After 3u 5u 8u
Before   3u + 46.5    5u                 
       

 

Then we look at the second if.

If 35.2 litre of water is drained out from Tank Y, the volume of the water in Tank Y will be 15% less than that of the water in Tank X.

  Tank X                 Tank Y            Total
After 3u 5u 8u
Before   3u + 46.5    5u   8u + 46.5 
After                3u + 46.5 5u – 35.2
Ratio

100%

85%
 

20

17

(3u + 46.5) / 20 = (5u – 35.2) / 17

17 x ( 3u + 46.5) = 20 * (5u – 35.2)        (Cross multiplication)

51u + 790.5 = 100u – 704

 790.5 + 704 = 100u – 51u

49u = 1494.5

1u = 30.5

8u = 244

244 + 46.5 = 290.50

 

Other same category question include

If A sells 100 cakes and B sells 200 cakes a day, A will have 300 cakes left when B sold all the cakes. If A sells 200 cakes and B sells 100 cakes, A will have 500 cakes left when B sold all the cakes. (Number are for example purpose)

 

0 Replies 1 Like
post-18256
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I have mental block too. Quite complex on these units and parts not being easy numbers. Just give it a go…  and don’t think MOE will be so harsh on the P6s. Don’t worry too much. But tables below are also useful tools to summarise if information is too much. Have a try with tables sometimes. 🙂  

    Tank X Tank Y Total
    ? ? ?
Case 1   -46.5    
    3u   8u
Case 2     -35.2  
    100% 85%  Note 1

Note 1: I didn’t feel like doing 20p, 17p, 37p and tying up the LCMs to solve…  Can try though…

Fill in the blanks…

    Tank X Tank Y Total
  Before 3u+46.50 5u 8u+46.50
Case 1   -46.5    
    3u   8u
  Before 100p 85p+35.2 185p+35.2
Case 2     -35.2  
   

100p

85p

185p

3u + 46.50 = 100p                 –> 15u + 232.50 = 500p

5u                = 85p +35.20     –> 15u                  = 255p +105.60

500p-232.50 = 255p+105.60

245p=338.10

p=1.38

Total = 185p+35.20 = 290.50 litres#


Solve  u=30.50 and check:

    Tank X Tank Y Total
  Before 138 152.50 290.50
Case 1   -46.5    
    91.5 (3 units) 152.50  244 (8 units)
  Before 138 152.50 290.50
Case 2     -35.2  
   

138 (100%)

117.30 (85%)

 

 

0 Replies 2 Likes

Scenario 1 (drain 46.5l from X)

X (after) : X(after)+Y -> 3:8

X(after) -> 3u

Y -> 5u

X (at first) -> 3u + 46.5

 

Scenario 2 (drain 35.2l from Y)

Y(after) -> 5u – 35.2

Also, Y(after) -> 15% less than X => 0.85 x (3u + 46.5) = 2.55u + 39.525

5u – 35.2 = 2.55u + 39.525

2.45u = 74.725

1u = 30.5

Total -> 8u + 46.5 = 8 x 30.5 + 46.5 = 290.5 litres

0 Replies 6 Likes