# Arithmetic - Ratio, Proportion & Variation - Previous Year CAT/MBA Questions

You can practice all previous year CAT questions from the topic Arithmetic - Ratio, Proportion & Variation. This will help you understand the type of questions asked in CAT. It would be best if you clear your concepts before you practice previous year CAT questions.

**CAT 1996 QA | Arithmetic - Ratio, Proportion & Variation**

The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.

- A.
Rs. 1.4 lakh

- B.
Rs. 2 lakh

- C.
Rs. 1 lakh

- D.
Rs. 2.1 lakh

Answer: Option C

**Explanation** :

Let the original weight of the diamond be 10x. Hence, its original price will be k(100x2) . . . where k is a constant.

The weights of the pieces after breaking are x, 2x, 3x and 4x. Therefore, their prices will be kx^{2}, 4kx^{2}, 9kx^{2} and 16kx^{2}. So the total price of the pieces = (1 + 4 + 9 + 16)kx^{2 }= 30kx^{2}. Hence, the difference in the price of the original diamond and its pieces = 100kx^{2} – 30kx^{2} = 70kx^{2} = 70000.

Hence, kx^{2} = 1000 and the original price = 100kx^{2 }= 100 × 1000 = 100000 = Rs. 1 lakh.

Workspace:

**CAT 1996 QA | Arithmetic - Ratio, Proportion & Variation**

Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than threefourths of the total number of matches, if it is true that no match can end in a tie?

- A.
4

- B.
6

- C.
5

- D.
3

Answer: Option A

**Explanation** :

The team has played a total of (17 + 3) = 20 matches. This constitutes $\frac{2}{3}$ of the matches. Hence, total number of matches played = 30. To win $\frac{3}{4}$ of them, a team has to win 22.5, i.e. at least win 23 of them. In other words, the team has to win a minimum of 6 matches (since it has already won 17) out of remaining 10. So it can lose a maximum of 4 of them.

Workspace:

**CAT 1993 QA | Arithmetic - Ratio, Proportion & Variation**

From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?

- A.
2 : 1

- B.
3 : 1

- C.
3 : 2

- D.
None

Answer: Option A

**Explanation** :

Let the two given numbers be x and y such that x > y.

According to the question,

x - $\frac{y}{2}=3\left(y-\frac{y}{2}\right)$

$\Rightarrow \frac{x}{y}=\frac{2}{1}.$

Workspace:

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