Question

Length of a rectangle is increased by 60% by what % would be breath be decreased b maintain the same area.

Answer 1

Let initially the length and breath be L and B respectively.

When length is increased by 60%.

New length = L + 60% of L

= L + 0.6L = 1.6L

Let the new breath be xB after decrement.

According to condition:

New Area = Old Area

1.6L * xB = L*B

1.6 * x = 1

x = 1 / 1.6

x = 0.625

Percent decrease in breath = (1 - x) * 100

= (1 - 0.625) * 100

= 0.325 * 100

= 32.5%

Hence, breath should be decreased by 32.5%

Answer 2

$\huge\mathfrak{Answer}$

Let the length 100 metre and breadth be 100m, then

New length = 160m, new breadth = x,

$\sf \: Then \: \: \: \: \: \: \: \: 160 \times x = 100 \times 100 \\ \\ \sf \implies \: x = \frac{100 \times 100}{160} \implies \: x = \frac{125}{2}$

$\therefore \: \rm \: decrease \: in \: breadth \: = 100 - \frac{125}{2} \% \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 37 \: \frac{1}{2} \%$

So the answer is 37 and 1/2 %