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X and Y share profits 3:2. Interest on drawings: X $550, Y $450 (at 5%). Profit for year: $94,000. Loan interest paid to X: $3,000. Each partner drew an amount equal to their salary. What was Y's share of residual profit?
Option B ($29,200) is correct.
X's salary = $550 ÷ 5% = $11,000; Y's salary = $450 ÷ 5% = $9,000
Residual profit = $94,000 − $3,000 + $1,000 − $11,000 − $9,000 = $73,000 (Interest on drawings added back: $550+$450=$1,000)
Y's share = 2/5 × $73,000 = $29,200
A particle is projected vertically upward with $u = 10\text{ m/s}$. Air exerts a resistive force $F = -0.2v^2$ on it ($m = 2\text{ kg}$, $g = 10\text{ m/s}^2$). The maximum height attained is:
Net force (taking up as positive): $F_{net} = -mg - 0.2v^2 = -20 - 0.2v^2$
Using $ma = v\dfrac{dv}{dx}$: $2v\dfrac{dv}{dx} = -20 - 0.2v^2$
Separating variables: $\dfrac{v\,dv}{20+0.2v^2} = -\dfrac{dx}{2}$
Integrating from $v = 10$ to $v = 0$: let $k = 20 + 0.2v^2$, $dk = 0.4v\,dv$
$\dfrac{1}{0.4}\big[\ln(20) - \ln(40)\big] = -\dfrac{H}{2} \Rightarrow H = \dfrac{2\ln 2}{0.4} = \mathbf{5\ln 2}$
Enzymes accelerate chemical reactions by:
Enzymes lower the activation energy (Eₐ) of a reaction, allowing more molecules to reach the transition state at a given temperature. They do not alter equilibrium.
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