Question 5 SSC CGL 2018 June 4 Shift 1

Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer

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Question 5 SSC-CGL 2018 June 4
[NOTE: only math questions solved]

Question: A truck covers a distance of 384 km ata certain speed. If the speed is reduced by 16 km / h, it will take two hours more to cover the same distance. What is the 75% of the original speed (in km / h)?

1. 54
2. 42
3. 45
4. 48

Method 1

If time to cover $\displaystyle 384 $ km was $\displaystyle T$ hours, then the distance lost while travelling slower by $\displaystyle 16$ km/h is $\displaystyle 16T$ km.

Or, $\displaystyle = 16 \times \frac{384}{v} = \frac{16 \times 384}{v}$ km

This distance is covered in $\displaystyle 2 $ hours.

By speed distance formula distance = speed x time, so $\displaystyle \frac{16 \times 384}{v} = (v - 16) \times 2$

Speeds according to the options are 54 x (4/3) = 72, 56, 60, 64 km/h

Speed should be such that LHS is a whole number, because RHS is a whole number.

Cycling, we see that only 64 meets this condition, hence we get (d) as the answer.

NOTE: we do not have to do a complete check. We should keep our mind open, like we have done above by observing that the LHS has to be a whole number.

Method 2

This method is based on the above concept.

If time to cover $\displaystyle 384 $ km was $\displaystyle T$ hours, then the distance lost while travelling slower by $\displaystyle 16$ km/h is $\displaystyle 16T$ km.

This distance is covered in 2 hours at a speed of $\displaystyle \frac{384}{T + 2}$. Note: the speed during the second journey is distance of 384/time of T + 2.

So $\displaystyle 16T = \frac{384}{T + 2} \times 2$

This will give a quadratic in T with T = 6, from where we obtain the speed as 384/6 = 64 km/h, and hence (d) as the answer.

Method 3

Let the speeds during the two journeys be v km/h and (v - 16) km/h respectively.

So difference of times during the two journeys can be written as $\displaystyle \frac{384}{v - 16} - \frac{384}{v} = 2$

Cycling through the options, or solving the equation, we again get (d) as the answer.

Method 4

We know for both journeys, distance of 384 = respective speed x respective time

We observe that $\displaystyle 384 = 64 \times 6$

Also that $\displaystyle 384 = 48 \times 8 \equiv (64 - 16) \times (6 + 2)$

We can infer that the original speed must be 64 and original time must be 6 hours.

Hence, once again, (d) is the answer!