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megha

· started a discussion

· 1 Months ago

doubt (Question: 116396.0 )

can u explain the last step

Question:
A tank has two compartments, I and II. Two taps X and Y, whose filling rates are in ratio of 2 : 1, are used to fill the tank. The ratio of the times taken by tap X to fill compartment I and tap Y to fill compartment II is 16 : 25. Find the ratio of the times taken by tap X to fill compartment II and tap Y to fill compartment I.
Options:
A) 25 : 64
B) 5 : 4
C) 4 : 5
D) 25 : 16
E) 64 : 25
Solution:
Ans: (a) Part I & II filled by tap x & y in constant time 
= 32 : 25

Then tap x & y will fill the part II & I tank in 

= \(\cfrac{25}{2}:32=25:64\)

Knowledge Expert

· commented

· 1 Months ago

Because the filling rates of X and Y are in the ratio of 2:1

megha

· commented

· 1 Months ago

how did 25x/2 come?

Knowledge Expert

· commented

· 1 Months ago

Let the time (in minutes) taken by tap X to fill compartment I be 16x and that taken by tap Y to fill compartment II be 25x. As the filling rates of X and Y are in the ratio of 2:1, the ratio of times they take to fill the same volume is 1:2.

So tap Y will take (16x)2 i.e. 32x minutes to fill compartment I and tap X will take 25x/2 i.e. 12.5x minutes to fill the compartment II.

Hence the ratio 12.5x:32x i.e. 25:64
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