If 𝑝 ∶ π‘ž = 1 ∶ 2 π‘ž ∶ π‘Ÿ = 4 ∶ 3 π‘Ÿ ∶ 𝑠 = 4 ∶ 5 and 𝑒 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑒?

If 𝑝 ∶ π‘ž = 1 ∶ 2 π‘ž ∶ π‘Ÿ = 4 ∶ 3 π‘Ÿ ∶ 𝑠 = 4 ∶ 5 and 𝑒 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑒?

Question: If 𝑝 ∶ π‘ž = 1 ∶ 2 π‘ž ∶ π‘Ÿ = 4 ∶ 3 π‘Ÿ ∶ 𝑠 = 4 ∶ 5 and 𝑒 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑒?

Solution:



Through the utilization of given ratios; the relationship between variables p, q, r and s can be established enabling us towards deducing the ratio of p:u which becomes possible after uncovering the value of variable u that is greater than s by a certain percentage. 

Taking into account provided ratios such as p∶q=1∶2 leads us towards being able to develop this equation where q=2p. 


After scrutinizing through q∶r =4∶3; r=(3 /4)q=(3/4)×2p =(3/2)p appears. Moreover when analyzing r ∶ 𝑠 = 4 ∶5. We determine that 𝑠 = (5 /4)π‘Ÿ = (5 /4)×(3/2)p =(15 /8)p. 


With regards to whats' stated about the relationship between variable u and s; it indicates how an increase of fifty percent greater than s occurs in its case thus making it becomes evident that

u=1.5s=1.5×(15/8)p=(45/16)p. 


By dividing both sides with greatest common factor equaling to one; we establish that:

π’Ž : 𝒖 =16𝑝 :45𝑝

 

Thus forming a final conclusion whereupon the ratio of p∶u equates to 16 : 45.

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About the Author

Mr Akhand Dutta is the Founder and Owner of Civil Engineering With Akhand Dutta (CEWA) and Akhand Dutta Writes. Currently, a civil engineering student at Bipin Tripathi Kumaon Institute of Technology, Dwarahat, Almora, Uttarakhand and has done his …

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