Question

(i) A certain sum was divided among A, B and C in the ratio 7: 5: 4. If B got Rs 500 more than C, find the total sum divided.

(ii) In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C Rs 80000 for 5 months. If they together earn Rs 18800 find the share of each.

Answer 1

$\left(i\right)$ It is given that

Ratio between $A,B$ and $C$ = $7:5:4$

Consider,

$A$ share = $7x$

$B$ share = $5x$

$C$ share = $4x$

So the total sum =$7x+5x+4x=16x$

Based on the condition

$5x–4x=500$

$x=500$

So the total sum =$16x=16\times 500=Rs8000$

$\left(ii\right)$ $1$ months investment of $A=Rs50000$

$6$ month investment of $A=50000\times 6=Rs300000$

$1$ months investment of $B=Rs60000$

$4$ month investment of $B=60000\times 4=Rs240000$

$1$ months investment of $C=Rs80000$

$5$ month investment of $C=80000\times 5=Rs400000$

Here the ratio between their investments = $300000:240000:400000=30:24:40$

Sum of ratio = $30=24+40=94$

Total earnings = $Rs18800$

So we get share of earning by each as ,

$A$ share = $\frac{30}{94}\times 18800=Rs6000$

$B$ share = $\frac{24}{94}\times 18800=Rs4800$

$C$ share = $\frac{40}{94}\times 18800=Rs8000$