Question

A farmer wanted to increase the cultivation area of the field. For this, he increased the length of the field by 30% but had to reduce the width by 15%. The area of the new field:

• A. Has increased by 15%
• B. Is exactly the same as the area of the old one
• C. Has increased by 10.5%
• D. Has increased by 22.5%

Answer 1

The correct option is C Has increased by 10.5%

Let the length of the field be l, and let the width of the field be b.
Original area will be, A = l $\times$ b
New length $=l\times (1+\frac{30}{100})=1.3l$
New width $=b\times (1-\frac{15}{100})=0.85b$
New area $=1.3l\times 0.85b=A\times (1.3\times 0.85)=A\times \frac{13}{10}\times \frac{17}{20}=\frac{221}{200}A$
New area is greater than the original area by $\frac{221}{200}A-A=\frac{21}{200}A$
% difference $=\frac{21}{200}\times 100=10.5\%$