# Quantitative Reasoning – Practice – Direct and Inverse Relation!

PSA_PRACTICE_QNR46. Thirty(30)cows were found to produce 650 kg of manure containing 10% Nitrogen in one week (7 days). You are required to help traditional smallholder farmers on their application requirement for 2 hectares of land planted with maize. how long will it take for the farmers to achieve 100 kg of Nitrogen if they have 50 cows?

Ans:

65 kg Nitrogen is contained in 650 kg manure.
5 kg Nitrogen is contained in 50 kg manure.
100 kg Nitrogen is contained in 1000 kg manure.

Initial condition: 30 cows, 650 kg manure, 7 days
Final conditions: 50 cows, 1000 kg manure, ? days

Let the number of days be ‘d’.

We will start with number of days as 7 and then action upon this number based upon other factors; other factors here include number of cows, and manure quantity.

Since the number of cows increases from 30 to 50, number of days will decrease. We would need to multiply ‘d’ with 30/50.
[Note that since the number of days is to decrease, the multiplying factor is 30/50 which is lesser than 1].

Thus, d= 7x (30/50)

Since the manure quantity increases from 650 kg to 1000 kg, number of days will increase. We would need to multiply ‘d’ with 1000/650.
[Note that since the number of days is to increase, the multiplying factor is 1000/650 which is greater than 1].

Thus, now d becomes = 7x (30/50) x 1000/650 = 7x (3/5) x 20/13 = 84/13 days.