# Quadratic Equations | Pipes Cistern

Ex 4.3 Q9. CBSE 10th Maths NCERT exercise solution

#### Question: Two water taps together can fill a tank in 9($$frac{3}{8}$) hours. The tap of larger dimensions takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. #### Video Explanation #### Explanatory Answer Step 1: Frame equations based on the information about the time taken by the two taps to fill the tank. Let the time taken by the tap of larger dimension be t hours. ∴ time taken by the tap of smaller dimension =$t + 10) hours.
The larger tap will fill $$frac{1}{t}$ of the tank in 1 hour The smaller tap will fill $\frac{1}{t + 10}$ of the tank in 1 hour Together the 2 taps will fill $\frac{1}{t}$ + $\frac{1}{t + 10}$ of the tank in 1 hour ----------$1)

Statement: Two water taps fill a tank in 9$$frac{3}{8}$ hrs i.e., in $\frac{75}{8}$ hours So, the taps will fill $\frac{1}{75/8}$= $\frac{8}{75}$ of the tank in 1 hour ----------$2)

Equate (1) and (2)
$$frac{1}{t}$ + $\frac{1}{t + 10}$ = $\frac{8}{75}$ Because t ≠ 0 and t cannot be -10, multiply the entire equation by t$t + 10)
(t + 10) + t = $$frac{8}{75}$$t (t + 10))
2t + 10 = $$frac{8}{75}$$t2 + 10t)
75(2t + 10) = 8t2 + 80 t
150t + 750 = 8t2 + 80 t
8t2 - 70t - 750 = 0
Divide the equation by 2 :
4t2 - 35t - 375 = 0

##### Step 2: Factorize to find the values of ‘t’

4t2 – 60t + 25t – 375 = 0
4t(t – 15) + 25 (t – 15) = 0
(4t + 25) (t – 15) = 0
t = $\frac{-25}{4}$ and t = 15
Time taken is positive
∴ t = 15 hrs and t + 10 = 15 + 10 = 25 hrs