NIMCET 2008 — Reasoning PYQ

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Question

NIMCET 2008 — Reasoning PYQ

NIMCET | Reasoning | 2008

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

Choose the correct answer:

Explanation

The most efficient way to solve this is using the Rule of Alligation. Let the weight of water be $w$ . Then the weight of gold is $19w$ , copper is $9w$ , and the required alloy is $15w$ .

1. Apply the Alligation Formula

We compare the densities of the two metals against the mean (target) density:

Density of Gold ( $G$ ): $19$
Density of Copper ( $C$ ): $9$
Target Density of Alloy ( $M$ ): $15$

The ratio of Gold to Copper is calculated as:

\text{Ratio (Gold : Copper)} = \frac{M - C}{G - M}

2. Calculation

Substitute the values into the formula:

\text{Ratio} = \frac{15 - 9}{19 - 15}

\text{Ratio} = \frac{6}{4}

3. Simplify the Ratio

Divide both numbers by their greatest common divisor, which is 2:

\frac{6}{4} = \frac{3}{2}

So, the metals should be mixed in the ratio of 3 : 2.

Final Answer

To achieve an alloy that is 15 times as heavy as water, gold and copper must be mixed in a ratio of 3 : 2.

The correct option is (c).