The ratio of the capacity of Tank A to that of Tank B is 7 : 3.Each tank is filled with some water.If the water from Tank B is poured into Tank A until it

Let x be the amount of water in tank A

Let m be the amount of water needed to fill tank A

So  the total capacity of tank A is (x+m)

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Let y be the amount of water in tank B

Let n be the amount of water needed to fill tank B

and the total capacity of tank B is (y+n)

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We are being asked to find (n+m)

Now the capacity ratio of tank A to tank B is 7:3  so

$$\begin{array}{rll} \frac{x+m}{y+n}&=&\frac{7}{3}\\\\ 3(x+m)&=&7(y+n)\\\\ \end{array}$$

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now there is x litres in tank A and m litres are needed to fill tank B so  

x-n=33 litres  ==>  x=33+n

Likewise

y-m=9 lites ==>  y=9+m

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$$\begin{array}{rll} 3(x+m)&=&7(y+n)\qquad \mbox{substituting for x and y we get;}\\ 3(33+n+m)&=&7(9+m+n)\\ 3*33+3(m+n)&=&7*9+7(m+n)\\ 99+3(m+n)&=&63+7(m+n)\\ 36&=&4(m+n)\\ 9&=&m+n\\ \end{array}$$

so the amount of water to fill up both tanks completely is 9L

Very nice, Melody!!! That was a tough one !!!

3 points from me.....

Thank you Chris,  we do make a good pair of colourful eggs.   ♬