There are three pumps P, Q and R with a tank. P. Q and R simultaneously can fill the tank in 5 hours. Again P and Q simultaneously can fill the tank in 7 hours. Then how many hours R need to fill the tank alone?

Shohan

8 views

2025-01-04 04:42

1 Answers

Shohan

$(P + R + T) t a k e 5 h o u r s t o f i l l u p 1 \tan k$

$∴ (P + R + T) t a k e 1 h o u r t o f i l l u p \frac{1}{5} p a r t o f \tan k$

$A g a i n, (P + R) t a k e 7 h o u r s t o f i l l u p 1 \tan k$

$∴ (P + R) t a k e 1 h o u r t o f i l l u p \frac{1}{7} p a r t o f \tan k$

$∴ I n 1 h o u r, T c a n f i l l u p = (\frac{1}{5} - \frac{1}{7}) = \frac{7 - 5}{35} = \frac{2}{35} p a r t o f \tan k$

$N o w, \frac{2}{35} o f \tan k i s f i l l e d b y T i n 1 h o u r$

$∴ 1 o r c o m p l e t e p a r t o f \tan k i s f i l l e d b y T i n = \frac{35 \times 1}{2} = 17 \frac{1}{2} h o u r s$

8 views Answered 2024-12-14 13:31

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