(solved)Question 5 SSC-CGL 2018 June 4 Shift 1

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)?

1. 54
2. 42
3. 45
4. 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

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.

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.

1. 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]
2. 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]