50 %
Let, Income of Malek is Tk. 100
Expenditure = Tk. 75 & Savings = 100 — 75 = Tk. 25
At 20% increase, New income = Tk. 120
& New expenditure = 75 + 75 x 10% = Tk. 82.5
New Saving = (120 – 82.5) = 37.5
% of increased amount of savings = $\frac{37.5-25}{25}x100\%$ = 50%
TK 108000
Let, Capital of C = Tk. x
Capital of B = Tk. 4x
Capital of A = $\frac{4x \cdot 3}{2}$ = 6x TK
Ratio of capital of A, B & C = 6x : 4x : x
= 6 : 4: 1
The share of profit of B= 297000 x $\frac{4}{6+4+1}$
= Tk. 108,000
See explanation
Given, $a-\frac{1}{a} =m$
=> $(a-\frac{1}{a})^{2} =m^{2}$
=> $a^{2}-2a\frac{1}{a}+(\frac{1}{a})^{2} =m^{2}$
=> $a^{2}+(\frac{1}{a})^{2} =m^{2}+2$
=> $(a^{2}+\frac{1}{a^{2}})^{2} =(m^{2}+2)^{2}$
=> $((a^{2})^{2}+2 a^{2}\frac{1}{a^{2}}+(\frac{1}{a^{2}})^{2} =m^{4}+2m^{2}2+2^{2}$
=> $a^{4}+\frac{1}{a^{4}}=m^{4}+4m^{2}+2$
256-64π
Side of the square ABCD = 16
% of the square ABCD =$\frac{16}{2}$ = 8
Radius of each circle = 8
Area of the shaded part = 16² — 4 x π 8² x$\frac{1}{4}$
= 256 — 64π
$\frac{3}{20}$
Let, Total member = x
Men= $\frac{2x}{3}$ and Women =x- $\frac{2x}{3}$ = $\frac{x}{3}$
Men from country Y= $\frac{2x}{3} \cdot \frac{3}{8} = \frac{x}{4}$
Member from country X =$\frac{3x}{5}$
Member from country Y = x — $\frac{3x}{5}$ = $\frac{2x}{5}$
Women from country Y = $\frac{2x}{5}$ – $\frac{x}{4}$
= $\frac{3x}{20}$
The required fraction = $\frac{\frac{3x}{20}}{x} = \frac{3}{20}$
30 minutes
Tap X in 20 minutes can fill 1 portion
Tap X in 10 minutes can fill =$\frac{10}{20}$=$\frac{1}{2}$ portion
Tap Y in 60 minutes can till 1 portion
Tap X in 10 minutes can fill $\frac{10}{60}$=$\frac{1}{6}$ portion
In 10 minutes tank filled = $\frac{1}{2}+\frac{1}{6}$ portion
= $\frac{2}{3}$
Remalnmg = 1 – $\frac{2}{3}$ = $\frac{1}{3}$ portion
Tap Y can fill 1 portion in 60 minutes
Tap Y can $\frac{1}{3}$ portion in 60 x $\frac{1}{3}$ = 20 minutes
Total time required = (10 + 20) = 30 minutes
