MATHEMATICS > Time and Distance
1) If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more in the same time. The usual distance travelled by him is :
A) 50 kmB) 56 km
C) 70 kmD) 80 km
View AnswerDiscuss on this        RRB_JE_2014_Answer-key
Answer : 50 km

\begin{aligned} \text{S1=10}\frac{km}{hr}\\ \text{S2=14}\frac{km}{hr}\\ \text{d1=x km}\\ \text{d2=x+20 km}\\ \frac{D1}{S1}=\frac{D2}{S2}\\ \frac{x}{10}=\frac{\left(x+20\right)}{14}\\ \text{14x=10x+200}\\ \text{4x=200} \text{X=50 km} \end{aligned}


2) A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long ?
A) 40 secB) 42 sec
C) 45 secD) 48 sec
View AnswerDiscuss on this        RRB_JE_2014_Answer-key
Answer : 40 sec

\begin{aligned} \text{L1 = 360 m}\\ \text{L2 = 140 m}\\ \text{S = 45 }\frac{km}{hr}\text{ = }\frac{45*5}{18}\frac {m}{s}\\ \text{T = }\frac{\left(360+140\right)}{\left(\frac{25}{2}\right)} sec\\ \text{T = } \left(\frac{500 * 2}{25}\right)\\ \text{T = 40 sec} \end{aligned}

3) A train of length 100 m runs at a speed of 120 km/h from north to south. Another train of length 150 m travels with a speed of 80 km from south to north. What is the time required to cross each other
A) 3.6 secB) 4 sec
C) 4.5 secD) 5.2 sec
View AnswerDiscuss on this        Sub Inspector Answer key
Answer : 4.5 sec

\begin{aligned} \text{T = relative length/relative speed}\\ \text{ T = }\frac{\left(100+150\right)}{\left(120+80\right)\left(\frac{5}{18}\right)}\\ =\frac{250}{\left(\frac{200*5}{18}\right)}\\ =\frac{5*18}{20}=\frac{9}{2}\\=4.5 sec \end{aligned}

4) Starting from a place P, a man travels 4 km towards North then turns towards right and travels 5 km. After that he turns towards right and travles 8 km. What is his current position with respect to P
A) 4 km towards EastB) 6 km towards South West
C) 4 km towards North EastD) 6 km towards Sout East
View AnswerDiscuss on this        Sub Inspector Answer key
Answer : 4 km towards East

4km south east so answer is None of the above

5) A car is running at a speed of 108 kmph. What distance will it cover in 15 seconds
A) 45 mB) 55 m
C) 450 mD) None of these
View AnswerDiscuss on this        CES General paper
Answer : 450 m

\begin{aligned} \text{S1 = 108 }\frac{km}{hr}\\ \text{T1 = 15 sec}\\ \text{S1 = }\left(\frac{108*5}{18}\right) \frac{m}{sec}\\ \text{= 30 }\frac{m}{s}\\ \text{D = S1*T1}\\ \text{D = 30 * 15 m}\\ \text{D = 450 m} \end{aligned}

6) A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5 km on foot His total journey distance is
A) 65 kmB) 100 km
C) 120 kmD) 130 km
View AnswerDiscuss on this        CES General paper
Answer : 130 km

\begin{aligned} \text{Total distance=x km}\\ \text{By rail=}\frac{3}{5}\text{(x),by bus=}\frac{17}{20}\text{(x) remaining=6.5 km}\\ \frac{3}{5}(x)+ \frac{17}{20}(x)+6.5=x\\ \frac{12+17}{20}(x)+6.5=x\\ \frac{29}{20}(x)+6.5=x\\ \text{29 (x) + 6.5 * 20 = 20x}\\ \text{29 - 20 (x) = - 130}\\ \text{X = }\frac{130}{9} \end{aligned}