Question : If the altitude of a triangle is increased by 10% while its area remains the same, its corresponding base will have to be decreased by:
Option 1: $10\%$
Option 2: $9\%$
Option 3: $9\frac{1}{11}\%$
Option 4: $11\frac{1}{9}\%$
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Correct Answer: $9\frac{1}{11}\%$
Solution : Given that the area remains the same and the altitude is increased by $10\%$, the base must decrease to compensate for this. Let the original base be $B_o$ and the original altitude be $A_o$. The new altitude is $1.1A_n$. Let the new base be $B_n$. $⇒\frac{1}{2} \times B_o \times A_o= \frac{1}{2} \times B_n \times 1.1A_n$ $⇒B_n = \frac{B_o}{1.1}$ The percentage decrease in base $=(\frac{B_o-B_n}{B_o})×100$ The percentage decrease in base $=(\frac{B_o-\frac{B_o}{1.1}}{B_o})×100$ The percentage decrease in base $=(1-\frac{1}{1.1})×100=9\frac{1}{11}\%$ Hence, the correct answer is $9\frac{1}{11}\%$.
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Question : If profit is $\frac{1}{11}$th of the selling price, what is the profit percentage?
Option 1: $9\frac{1}{11}\%$
Option 2: $10\%$
Option 3: $8\frac{1}{3}\%$
Question : The base of a triangle is 16 cm and its area is 144 cm2. Find its corresponding height, with respect to the given base.
Option 1: 18 cm
Option 2: 9 cm
Option 3: 24 cm
Option 4: 12 cm
Question : If the radius of a cylinder is decreased by 12%, then by how much percentage must its height be increased so that the volume of the cylinder remains the same?
Option 1: 29.13%
Option 2: 21.78%
Option 3: 42.56%
Option 4: 34.27%
Question : The radius of a circle is increased by 10%. The percentage increase in its area is:
Option 1: 10%
Option 2: 11%
Option 3: 20%
Option 4: 21%
Question : If $A=\frac{2}{3} \div \frac{4}{9}, B=\frac{6}{11} \times\frac{33}{12}$ and $C=\frac{1}{3} \times \frac{9}{2}$, then what is the value of $A \times B-C$?
Option 1: $\frac{3}{8}$
Option 2: $\frac{3}{2}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{3}{16}$
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