NIMCET 2008 — Reasoning PYQ

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Question

NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers Raja and Rahim have 60 kg luggage between them, and are charged ₹ 1200 and ₹ 2400, respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been ₹ 5400. What is the weight of Rahim’s luggage?

Choose the correct answer:

Explanation

Let:

$x$ = Free luggage allowance per person (in kg).
$r$ = Rate charged per kg for excess luggage (in ₹/kg).
$w_1$ = Weight of Raja’s luggage.
$w_2$ = Weight of Rahim’s luggage.

From the question, we know:

$w_1 + w_2 = 60$
Raja's charge: $r(w_1 - x) = 1200$
Rahim's charge: $r(w_2 - x) = 2400$
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(w_1 - x) + r(w_2 - x) = 1200 + 2400

r(w_1 + w_2 - 2x) = 3600

Since $w_1 + w_2 = 60$ :

r(60 - 2x) = 3600 \quad \text{--- (Equation 1)}

Step 2: Use the "entire luggage" scenario.

We already have:

r(60 - x) = 5400 \quad \text{--- (Equation 2)}

Step 3: Solve for $x$ (Free Allowance).

Divide (Equation 2) by (Equation 1):

\frac{r(60 - x)}{r(60 - 2x)} = \frac{5400}{3600}

\frac{60 - x}{60 - 2x} = \frac{3}{2}

2(60 - x) = 3(60 - 2x)

120 - 2x = 180 - 6x

4x = 60 \implies x = 15 \text{ kg}

Step 4: Solve for Rahim's weight ( $w_2$ ).

Substitute $x = 15$ back into Rahim's charge equation and the rate comparison.

From Equation 2: $r(60 - 15) = 5400 \implies 45r = 5400 \implies r = 120$ ₹/kg.

Now, use Rahim’s individual charge:

r(w_2 - x) = 2400

120(w_2 - 15) = 2400

w_2 - 15 = \frac{2400}{120}

w_2 - 15 = 20

w_2 = 35 \text{ kg}

Final Answer:

The weight of Rahim's luggage is 35 kg.

Correct Option: (d) 35 kg