### Query Detail : RBI Grade B Phase I

**Train A crosses a pole in 12 sec and train B crosses train A in 178 sec while running in same direction. If ratio of speed of train A to that of train B is 12:13 and train A is 100 m long than train B, then find in how many seconds train B will cross a pole?**

Garima,
November 8th 2019,

RBI Grade B Phase I

**
**

**Let Speed of train A = 12x and Speed of train B = 13x**

& Let length of train B = L So length of train A = L+100

So 12x = (L+100)/12 or L+100 = 144x or L = 144x-100--(1)

and (13x- 12x) = (L+L+100)/178s

x = (2L+100)/178

x ={2(144x-100)+100}/178

178x = 288x - 200 + 100 = 288x - 100

288x -178x = 100

110x = 100

or x = 100/110

So L = 144x - 100 = 144*100/110 - 100 = (14400-11000)/110 = 3400/110 = 340/11m

So train B will cross a pole in = L/13x = (340/11)/(13*100/110) = 340 * 110 /(13*11*100)

= 34/13 seconds