dhairya275 wrote:A garden has only red, green and yellow flowers, 57% of the flowers have red colour, 35% have green colour and 50% have yellow colour.If no flower has all three colors, what percentage of the flowers has only one colour?
[A] 32
50
[C] 55
[D] 58
[E] 82
100% = R + G + Y - (RG + RY + GY)
SUBTRACT THE OVERLAP.
In the equation above, when we count all of the red flowers (R), all of the green flowers (G), and all of the yellow flowers (Y), the OVERLAP -- every flower that has exactly TWO colors -- gets counted TWICE.
Thus, we SUBTRACT these flowers (RG + RY + GY) from the total so that they are not double-counted.
Plugging the given percentages into the equation above, we get:
100 = 57 + 35 + 50 - (RG + RY + GY)
RG + RY + GY = 42.
Since 42% of the flowers have exactly two colors, the percentage that have only one color = 58%.
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