Question

Divide Rs. 4,260 into three parts proportional to $2\frac{1}{2}:1\frac{2}{3}:1\frac{3}{4}$.

• A. Rs. $1,800$ ; Rs.$1,200$ and Rs.$1,260$
• B. Rs.$1,600$ ; Rs.$1,200$ and Rs.$1,260$
• C. Rs.$1,800$ ; Rs.$1,200$ and Rs.$1,280$
• D. Rs.$1,800$ ; Rs.$1,400$ and Rs.$1,260$

Answer 1

The correct option is A Rs. $1,800$ ; Rs.$1,200$ and Rs.$1,260$

The given proportion is $2\frac{1}{2}:1\frac{2}{3}:1\frac{3}{4}=\frac{5}{2}:\frac{5}{3}:\frac{7}{4}$.
Now multiply with $\frac{6}{6},\frac{4}{4},\frac{3}{3}$ so all denominator become same .
$\frac{5}{2}\times \frac{6}{6}=\frac{30}{12}$
$\frac{5}{3}\times \frac{4}{4}=\frac{20}{12}$
$\frac{7}{4}\times \frac{3}{3}=\frac{21}{12}$
Now we have proportion $30:20:21$
Total of all proportion $30+20+21=71$
Now Profit of 1st Part $=\frac{30}{71}\times 4260=1800$
Profit of 2nd Part $=\frac{20}{71}\times 4260=1200$
Profit of 3rd Part $=\frac{21}{71}\times 4260=1260$