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Pipes and Cisterns
Aptitude Shortcuts

Shortcut of Pipes and Cisterns

Shortcut 73: One pipe fills and another empties [latex]\frac{AB}{-A+B}[/latex] Question: Pipe A can fill a tank in 4 hours and pipe B can empty the tank in 5 hours. If both pipes are opened together, how long will they take to fill a complete tank? Answer: A = 4 B = 5 Substitute the values

time and work
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Shortcut of Time and work-3

Shortcut 68: Three men working together [latex] \frac{ABC}{AB+BC+AC}[/latex] Question: A can do a work in 40 days, B in 50 days and C in 60 days. If they work together, how long will they take to complete the work? Answer: A = 40 B = 50 C = 60 Substitute the values in the above

time and work
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Shortcut of Time and work-2

Shortcut 65: Time, Work and Resource [latex]\frac{W_1}{W_2}=\frac{R_1T_1}{R_2T_2} [/latex] Question: If 10 men can cut 40 trees in 4 days, how many trees can be cut by 40 men 6 days? Answer: R1 = 10; R2 = 40 T1 = 4; T2 = 6 W1 = 40; W2 = ? Substitute the values in the above

time and work
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Shortcut of Time and work-1

Shortcut 62: Time taken is directly proportional to work. [latex]\frac{W_1}{W_2}=\frac{T_1}{T_2} [/latex] Question: It took 40 days to build 10 buildings. How long will it take to build 50 buildings using same number of employees? Answer: W1 = 10; W2 = 50 T1 = 40; T2 = ? Substitute the values in the above formula, we

Boats
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Shortcut of Boats

Boats Shortcut 59: Time taken upstream     [latex]T=\frac D{S_b-S_r} [/latex] Question: The speed of boat in still water is 40kmph. How long will the boat take to row 175 km upstream in a river of speed 5kmph? Answer: D = 175km Sb = 40kmph, (speed of boat in still water) Sr = 5kmph, (speed of

Trains
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Shortcut of Trains-2

Shortcut 55: Train crossing a man on another train in same direction [latex]T=\frac{L_T}{S_1\sim S_2} [/latex] Question: Two trains A and B of length 100m and 200 are travelling at a speed of 72kmph and 54kmph respectively in same directions. How long will train A take to cross a man travelling in train B? Answer: LT

Trains
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Shortcut of Trains-1

Shortcut 50: Train crossing a pole   [latex]T=\frac{L_T}{S_T} [/latex] Question: A train of length 450m is travelling at a speed of 54kmph. How long will it take to cross a pole? Answer: Speed of train ST in m/s = 54x(5/18) = 15mps Length of train = LT = 450m Time taken to cross = 450/15

Time, Speed and Distance
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Shortcut of Time, Speed and Distance-2

Shortcut 45: Average speed when distances are same                   [latex]S_a=\frac{2S_1S_2}{(S_1+S_2)}[/latex] Question: Sai travels from her house to office at a speed of 50kmph. She suddenly returns home at a speed of 60kmph. What is her average speed? Answer: S1 = 50 S2 = 60 Sa = 2(50×60)/(50+60) = 6000/110 = 54.54 kmph Shortcut 46: Average

Time, Speed and Distance
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Shortcut of Time, Speed and Distance-1

Shortcut 40:     [latex]S=\frac DT[/latex] S = Speed D = Distance T = Time taken Question: A man travels 200 km in 4 hours. What is the speed in which he travelled? Answer: S = 200/4 = 50 kmph Question: A cat runs at a speed of 3 meter per second. How long will it

Problems on Ages
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Shortcut of Problems on Ages

Shortcut 37:                          One Variable Linear Equation Question: Age of father is twice that of son at present. After 5 years, sum of their ages will be 100. What is the present age of father? Answer: Assume age of son = S Age of father = 2S Age of father after 5 years = 2S

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