Mathematics Problem Solving Group

A. 16% B. 20% C. 24% D. 25% UPSC CDS 1 2021 Elementary Matematics Solution: It is given that CP of 100 Mangoes = SP of 80 Mangoes. Let CP and SP be Cost Price and Selling Price of 1 Mango. We can write that, 100CP = 80SP SP = 100CP/80 SP = 5CP/4 We know that Profit % = ((SP - CP)/CP) * 100 Profit % = ((5CP/4 - CP)/CP) * 100 Profit % = (1/4) * 100 Profit % = 25 % Hence, (d) is the correct answer.

A. 48 minutes B. 50 minutes C. 54 minutes D. 60 minutes UPSC CDS 1 2021 Elementary Mathematics Paper Solution: Let us have a look at the shortcut method: Ratio of usual speed to 4/5th speed = 5 : 4 As distance is the same, ratio of usual time to time taken at 4/5th speed = 4 : 5 A difference of 1 unit of time corresponds to 12 minutes time difference, therefore, 4 units of time (usual time) will be 4 * 12 = 48 minutes. Hence, (a) is the correct answer. Let us have a look at the basic approach: Let the usual speed of man be x km/minute. Let the usual time taken by the man be t minutes. Let the distance be d km. We know that, speed = distance/time x = d/t d = x.t .......(1) If the speed of man becomes 4x/5 km/minute, then the time taken by the man will be (t - 12) minutes Using, speed = distance/time 4x/5 = d/(t - 12) d = 4x.(t - 12)/5 ....(2) Equating equation 1 and 2, we get x.t = 4x.(t - 12)/5 t = 4(t - 12)/5 5t = 4t - 48 t = 48 minutes. Hence, (a) is the correct answer. This is a qu...