Let:
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x = Free luggage allowance per person (in kg).
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r = Rate charged per kg for excess luggage (in ₹/kg).
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w1 = Weight of Raja’s luggage.
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w2 = Weight of Rahim’s luggage.
From the question, we know:
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w1+w2=60
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Raja's charge: r(w1−x)=1200
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Rahim's charge: r(w2−x)=2400
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Total charge if one person had all 60 kg: r(60−x)=5400
Step 1: Find the relationship between Raja and Rahim's excess weight.
Adding the two individual charges:
r(w1−x)+r(w2−x)=1200+2400
Since w1+w2=60:
r(60−2x)=3600— (Equation 1)
Step 2: Use the "entire luggage" scenario.
We already have:
r(60−x)=5400— (Equation 2)
Step 3: Solve for x (Free Allowance).
Divide (Equation 2) by (Equation 1):
r(60−2x)r(60−x)=36005400
Step 4: Solve for Rahim's weight (w2).
Substitute x=15 back into Rahim's charge equation and the rate comparison.
From Equation 2: r(60−15)=5400⟹45r=5400⟹r=120 ₹/kg.
Now, use Rahim’s individual charge:
Final Answer:
The weight of Rahim's luggage is 35 kg.
Correct Option: (d) 35 kg
