Manav starts from a place A and reaches the place B in 29 hours. He travels 2/9 distance at the speed of 9 km/hr and the remaining distance at the speed of 12 km/hr. What is the distance between A and B?

a) 376 km
b) 208 km
c) 324 km
d) 264 km

Ans : c) 324 km

SSC Constable GD Exam Paper – Elementary Mathematics

Solution:

Let’s solve this step-by-step:

Let the total distance between A and B be ( D ) km.

Distance traveled at 9 km/hr: $ \text{Distance} = \frac{2}{9}D $
$ \text{Time taken} = \frac{\frac{2}{9}D}{9} = \frac{2D}{81} \text{ hours} $

Distance traveled at 12 km/hr: $ \text{Distance} = D – \frac{2}{9}D = \frac{7}{9}D $
$ \text{Time taken} = \frac{\frac{7}{9}D}{12} = \frac{7D}{108} \text{ hours} $

Total time taken: $ \frac{2D}{81} + \frac{7D}{108} = 29 \text{ hours} $

Finding a common denominator (324): $ \frac{8D}{324} + \frac{21D}{324} = 29 $
$ \frac{29D}{324} = 29 $

Solving for ( D ): $ 29D = 29 \times 324 $
$ D = 324 \text{ km} $

So, the distance between A and B is 324 km.