From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
175 and 200
Train speed is 54/3.6 = 15 m/s. Relative to the runner, its speed is (54−9)/3.6 = 12.5 m/s, so train length is 12.5 × 14 = 175 m. Total distance across the platform is 15 × 25 = 375 m, giving platform length 200 m.
Important Questions from Numerical Computation
If \({\left( {z + \frac{1}{z}} \right)^2} = 98\), compute \(\left( {{z^2} + 1/\;{z^2}\;} \right)\)
- In the context of measures of surfaces, which one of the following is $not$ correct?
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?
