If 18 pumps can raise 2170 tonnes of water in 10 days working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water working 9 hours a day? A) 6 B) 7 C) 8 D) 9
ANSWER
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Hint: To solve this problem we need to have knowledge on work and time concept. In this problem we have to find how many days 16 pumps raise to 1736 tonnes of water in 9 hours before this we have to find the work for 1 day.
Complete step-by-step answer: According to the given data, we know that 18 pumps raise 2170 tonnes of water in 10 days working 7 hours a day. Before finding the calculation of 16 pumps let us find for 1pump, 1day and 1hour to make our solution easy. We know that in 10days there is rise of 2170 tonnes of water 10 days =2170 tonnes of water 1 day =$\dfrac{{2170}}{{10}} = 217 $ tonnes Then for 1hour we can raise 1hour = $\dfrac{{217}}{7} = 31$ tonnes (since the work has done for 7 hours) Then for 1 pump we can raise, 1 pump = $\dfrac{{31}}{{18}}$ tonnes Now let us calculate actual problem Since we know that 1 pump raises $\dfrac{{31}}{{18}}$ tonnes of water. Then 16 pumps will raise = $\dfrac{{31}}{{18}} \times 16$ tonnes. Then working for 9 hours a day will raise =$\dfrac{{31}}{{18}} \times 16 \times 9$ tonnes Now for d no. of days it will raise =$\dfrac{{31}}{{18}} \times 16 \times 9 \times d$ The total number of tonnes given for 16 pumps = 1736 tonnes The total number tonnes =its work 1736 = $\dfrac{{31}}{{18}} \times 16 \times 9 \times d$ $ \Rightarrow d = \dfrac{{1736 \times 18}}{{9 \times 16 \times 31}} = 7$ Therefore the total required number of days that will raise 1736 tonnes of water is 7 days. Option B is the correct answer.
Note: This problem can also be solved by using formula, the required formula is \[\dfrac{{p_1 \times h_1 \times d_1}}{{w_1}} = \dfrac{{p_2 \times h_2 \times d_2}}{{w_2}}\].Here p denotes number of pumps, h denotes number hours, d denote number of days, w denotes work (tonnes of water). And 1 and 2 denotes case 1 and case 2. On substituting the value we get the answer as 7 days.