### Question 5

SSC-CGL 2018 June 4 Shift 1

A truck covers a distance of 384 km at a 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)?

- 54
- 42
- 45
- 48

### Solution Simple and Direct

384 km has been covered in two ways with speeds differing by 16 kph, and the respective times by 2 hours.

We know distance = speed x time.

Can we factorize 384 in two ways where the factors differ by 16 and 2?

[1] By inspection, $\displaystyle 384 = 64 \times 6$

[2] Likewise, $\displaystyle 384 = 48 \times 8$

We can safely say that 64 and 48 are the two speeds differing by 16 kph whereas 6 and 8 can represent the respective times differing by 2 hours!

75% of 64 gives 48 kph as the answer!

### Comments and Discussion

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### Solution in Detail

Speed during first journey = $\displaystyle v$ kph.

$\displaystyle \therefore $ time taken $\displaystyle = \frac{384}{v}$ hour.

During the second journey, the speed of the truck is reduced by 16 kph.

So, speed = $\displaystyle v - 16$ kph.

Distance remains same at 384 km.

$\displaystyle \therefore $ time taken $\displaystyle = \frac{384}{v - 16}$ hour.

Difference of times during the two journeys has been given as 2 hours.

$\displaystyle \therefore \frac{384}{v - 16} - \frac{384}{v} = 2$

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

### Solution by Alternate Approach

⚠️ May be tougher for non-engineers. Given here only for academic interest. 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.### Solution 3 Aliter

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.

### Practice Exercise

Solve these questions based on the same concept.

- Shradha spent Rs. 500 to buy notebooks for her. If the price per notebook is increased by Rs. 10, she can buy 25 notebooks less. What was 50% of the original price? [Write your answer in the comments section below]
- Two milk samples weigh 12 kg. The volume of the second sample is 3 litres more, whereas it is lighter [density] by 2kg/liter. What is the density of the first sample?[Write your answer in the comments section below]

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