Question: A truck travelling at 70 kilometres per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kilometres per hour. If the truck can travel 19.5 kilometres on a litre of diesel at 50 kilometres per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kilometres per hour?
(A) 130
(B) 140
(C) 150
(D) 175
(E) 180
“A truck travelling at 70 kilometres per hour uses 30% more diesel to ''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section tests the mathematical skills and numerical literacy of the candidates. The candidates must choose the correct option by solving the quantitative problems with mathematical understanding. The students must possess basic knowledge of quantitative to solve GMAT Problem Solving questions. The GMAT Quant topic cites mathematical problems in the problem-solving part that ought to be solved with better qualitative skills.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- A truck travelling at 70 kmph uses 30% more diesel to cover a certain distance than it travels at 50 kmph
- The truck travels 19.5 km on a litre of diesel at 50 kmph
Find Out:
- The distance covered by the truck on 10 litres of diesel at 70 kmph
The truck can cover a distance of 19.5 km per litre of diesel at a speed of 50 kmph.
Therefore, in 10 litres, the truck can cover a distance of 19.5 x 10 = 195 km
This distance therefore should be 30% more than the distance covered by the truck at a speed of 70kmph
Thus, at a speed of 70kmph, the truck can cover a distance of= 195/1.3 ( since, 30% more means 130/100 = 1.3) = 150 km
Hence, the distance covered by the truck on 10 litres of diesel at 70 kmph = 150 km
Correct Answer: (C)
Approach Solution 2:
The problem statement states that:
Given:
- A truck travelling at 70 kmph uses 30% more diesel to cover a certain distance than it travels at 50 kmph
- The truck travels 19.5 km on a litre of diesel at 50 kmph
The question asked to find the distance covered by the truck on 10 litres of diesel at 70 kmph.
Let initial velocity (v1) and final velocity (v2) be 70kmph and 50kmph respectively.
Let’s assume that amount of diesel used is D.
Therefore, the initial diesel (D1) used by the truck is the sum of the final diesel (D2) and 30% of the final diesel used.
That is we can say, D1= D2 + 30% D2
Thus in the next step, we can get, D1= (13/10)D2
Now, the question states that D2 is 1 litre then D1 is 1.3 litre.
Therefore, we can say, when 1.3 litres is consumed by the truck, it goes 19.5 km at a speed of v1 i.e 50kmph
Therefore, when 10 litres is consumed by the truck, then it goes x km.
Thus, the value of x = 10*19.5/1.3
Therefore, x = 150 km
Hence, the distance covered by the truck on 10 litres of diesel at 70 kmph = 150 km
Correct Answer: (C)
Approach Solution 3:
The problem statement states that:
Given:
- A truck travelling at 70 kmph uses 30% more diesel to cover a certain distance than it travels at 50 kmph
- The truck travels 19.5 km on a litre of diesel at 50 kmph
Asked:
- Find the distance covered by the truck on 10 litres of diesel at 70 kmph.
Distance covered by the truck on 1 litre of fuel at 50 kmph= 19.5 km
To cover 19.5 km at the rate of 70kmph, the truck uses 30% more fuel that is = 1.3 litres
Therefore, at the rate of 70kmph and with 1 litre of fuel, the truck cover 19.5/1.3 = 15 km
Hence, the distance travelled by truck at 70kmph with 10litres of fuel= 10 x 15 = 150 km
Correct Answer: (C)
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