Coachify CAT Club
Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
Text Explanation:
Let the volume be 20 units
So A fills at 4 units/hr
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
In a $\triangle ABC,D,E$ and $F$ are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a $\triangle DEF$ and the area of a $\triangle ABC$ is:
We are given :
Now In triangle ABC
using the mid point theorem
we get DE || BC and DE = $\frac{1}{2}\left(BC\right)$
Now ADE is similar to ABC
So Area of ADE : Area of ABC = (DE/BC)^2 = 1:4
Similarly Area of BDF :Area of ABC = 1:4
and Area of CEF : Area of ABC = 1:4
Now we can say if area of ABC = 4A
then area of ADE = area of BFD = area of CEF = a
Therefore area of DEF = 4a-3a =a
so area of DEF : area of ABC = 1:4