Question

What is the weight of Praja's luggage?

• A. 20 kg
• B. 25 kg
• C. 30 kg
• D. 35 kg
• E. 40 kg
• A. 10 kg
• B. 15 kg
• C. 20 kg
• D. 25 kg
• J. 30 kg

Answer 1

The Correct Option is D

Let the free luggage allowance be $F$ kg and the charge per kg be $r$ Rs. For Raja: $(W_R - F) r = 1200$ → $W_R - F = \frac{1200}{r}$ For Praja: $(W_P - F) r = 2400$ → $W_P - F = \frac{2400}{r}$ We also know: $W_R + W_P = 60$ If one person carried all: $(60 - F) r = 5400$ → $60 - F = \frac{5400}{r}$ Subtract first eqn from the combined eqn: \[ (60 - F) - (W_R - F) = \frac{5400}{r} - \frac{1200}{r} \Rightarrow 60 - W_R = \frac{4200}{r} \] But $W_P = 60 - W_R$ → $W_P = \frac{4200}{r}$ From $W_P - F = \frac{2400}{r}$, we have $F = \frac{4200 - 2400}{r} = \frac{1800}{r}$. Also from $60 - F = \frac{5400}{r}$: $60 - \frac{1800}{r} = \frac{5400}{r}$ → $60 = \frac{7200}{r}$ → $r = 120$. Thus $W_P = \frac{4200}{120} = 35$ kg. \[ \boxed{35 \ \text{kg}} \]

Answer 2

From Q58 we found $r = 120$ Rs/kg and $F = \frac{1800}{r} = \frac{1800}{120} = 15$ kg. \[ \boxed{15 \ \text{kg}} \]