Question

Divide ₹782 among P, Q and R in the ratio $$\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$$.

[Hint : Given ratio = 6 : 8 : 9.]

Answer 1

The given ratio is $$\frac{1}{2} : \frac{2}{3} : \frac{3}{4}$$. 

L.C.M. of denominators 2, 3 and 4 is 12. 

Multiply each fraction by 12:

$$\left(\frac{1}{2} \times 12\right) : \left(\frac{2}{3} \times 12\right) : \left(\frac{3}{4} \times 12\right) = 6 : 8 : 9$$ 

Sum of ratio terms = $$6 + 8 + 9 = 23$$. 

P's share = $$₹\left(782 \times \frac{6}{23}\right)$$

$$= ₹(34 \times 6)$$

$$= \text{₹ } 204$$

Q's share = $$₹\left(782 \times \frac{8}{23}\right)$$

$$= ₹(34 \times 8)$$

$$= \text{₹ } 272$$

R's share = $$₹\left(782 \times \frac{9}{23}\right)$$

$$= ₹(34 \times 9)$$

$$= \text{₹ } 306$$