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Question

A vessel has two electrical coils connected in parallel. When one coil is switched on it takes 30 minutes to boil a given amount of water. When other coil is switched on it takes 60 minutes to boil same water. If both coils are switched on simultaneously, what time will it take to boil same amount of water?

A
30 minutes
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B
20 minutes
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C
10 minutes
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D
40 minutes
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Solution

The correct option is B 20 minutes
Let H be the amount of heat required to boil the given water.

H=V2R1t1V2R1=Ht1
H=V2R2t2V2R2=Ht2

When two coils are switched on,

1R=1R1+1R2
V2R=V2R)1+V2R2
Ht=Ht1+Ht2
1t=1t1+1t2
t=t1×t2t1+t2=30×6030+60=20 min

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