Arithmetic

Ratio, Proportion & Variation

Medium

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$ . The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$ . Then Anjali's score exceeded Rama's score by

$32$

$35$

$24$

$26$

✅ Correct Option: 1

Let us represent the original scores with variables:

Rama's original score = R

Mohan's original score = M

Anjali's original score = A

Rama's score was one-twelfth of the sum of Mohan's and Anjali's scores:

$R = \frac{1}{12}(M + A)$

After each score increased by 6, the ratio became 11:10:3 (Anjali : Mohan : Rama).

When we have a ratio like 11:10:3, it means:

Anjali's revised score = 11x (for some value x)

Mohan's revised score = 10x

Rama's revised score = 3x

Since each score increased by 6, the original scores were:

Anjali's original score = 11x - 6

Mohan's original score = 10x - 6

Rama's original score = 3x - 6

Substituting into our first equation:

$R = \frac{1}{12}(M + A)$

$(3x - 6) = \frac{1}{12}[(10x - 6) + (11x - 6)]$

$3x - 6 = \frac{1}{12}(21x - 12)$

$3x - 6 = \frac{21x - 12}{12}$

$12(3x - 6) = 21x - 12$

$36x - 72 = 21x - 12$

$36x - 21x = 72 - 12$

$15x = 60$

$x = 4$

Now we can find the original scores:

Anjali's original score = 11x - 6 = 11(4) - 6 = 44 - 6 = 38

Rama's original score = 3x - 6 = 3(4) - 6 = 12 - 6 = 6

The difference = 38 - 6 = 32

Therefore, Anjali's score exceeded Rama's score by 32.

CAT 2020 Slot 2

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is $3: 2$ , while the ratio of the shares of Sunil and Mita is $4: 5$ . If the difference between the largest and the smallest of these three shares is Rs $400$ , then Sunil's share, in rupees, is

CAT 2019 Slot 2

The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$ , and in the ratio $3:4:3$ in $2015$ . If Ramesh's salary increased by $25\%$ during $2010-2015$ , then the percentage increase in Rajesh's salary during this period is closest to:

CAT 2024 Slot 2

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3: 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

CAT 2024 Slot 3

Rajesh and Vimal own $20$ hectares and $30$ hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of $5 : 3$ . If the total cultivation area of wheat and mustard are in the ratio $11: 9$ , then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

CAT 2023 Slot 3

The number of coins collected per week by two coin-collectors $A$ and $B$ are In the ratio $3:4$ . If the total number of coins collected by $A$ in $5$ weeks is a multiple of $7$ , and the total number of coins collected by $B$ in $3$ weeks is a multiple of $24$ , then the minimum possible number of coins collected by $A$ in one week is

2025 Slot 2

The ratio of expenditures of Lakshmi and Meenakshi is $2:3$ , and the ratio of income of Lakshmi to expenditure of Meenakshi is $6:7$ . If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is $4:9$ , then the ratio of their incomes is

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 666. The revised scores of Anjali, Mohan, and Rama were in the ratio 11:10:311:10:311:10:3. Then Anjali's score exceeded Rama's score by

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by $6$ . The revised scores of Anjali, Mohan, and Rama were in the ratio $11:10:3$ . Then Anjali's score exceeded Rama's score by