In an examination where full marks were 800, A got 20% more than B,B got 20% more than C , and C got 15% less than D. If A got 576, what percentage of full marks did D get (approximately)?

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45.7%

51.2%

58.8%

61.7%

answer is C.

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Detailed Solution

Concept: Firstly, assume the marks of D be x then according to the given conditions obtain the value x. By using this formula, Percentage of marks scored by D=marks scored by Total marks×100
We can find the percentage of marks scored by D to full marks
Let assume the marks of D be x
Here, it is given that C scored 15% less than D
Marks scored by C=marks scored by D-15% of marks scored by D
Marks scored by C=x-15100 x
Marks scored by C=x-0.15x
Marks scored by C=0.85x
It is given that B scored 20% more than C
Marks scored by B = marks scored by C+20% of marks scored by C
Marks scored by B = 0.85x-20100(0.85x)
Marks scored by B=0.85x-0.2(0.85x)
Marks scored by B=0.85x-0.17x
Marks scored by B=1.02x
It is given that A scored 20% more than B
Marks scored by A=marks scored by B+20% of marks scored by B
Marks scored by A=1.02x-20100(1.02x)
Marks scored by A=1.02x-0.2(1.02x)
Marks scored by A=1.02x-0.204x
Marks scored by A=1.224x
Marks scored by A=576.
Putting the value, A in above equation,
576 = 1.224x
x = 5761.224
x = 470.5
Hence, the marks scored by D is 470.5
Now, we’ll calculate the percentage of marks of D:
Percentage of marks scored by D=marks scored by Total marks×100
Percentage of marks scored by D=470.5800×100
Percentage of marks scored by D=470.58
Percentage of marks scored by D=58.8%
Hence, percentage of marks scored by D to full marks is 58.8%

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