Ratio & Proportion Questions for CAT with Answers PDF

Let n be the number of years served by the second.

 = 


64n + 272 = 81n
n = 16 years
First person's service = 16 - 9 = 7 years

Ratio of monthly incomes of Vasu and Ravi = 7 : 8
Let their incomes be 7x and 8x, respectively.
Ratio of their expenditures = 3 : 4
Expenditure = Income - Savings
Savings of Vasu = Rs. 2,400
His expenditure = (7x - 2,400)
Savings of Ravi = Rs. 1,600
His expenditure = (8x - 1,600)
According to question:

⇒ 28x - 9,600 = 24x - 4,800
⇒ 4x = 4,800
⇒ x = 1,200
Monthly income of Ravi = 8x = (8 × 1,200) = Rs. 9,600

Money invested by Suman for 12 months = Rs. 50,000
Money invested by Manu for 9 months = Rs. 75,000
Money invested by Amandeep for 6 months = Rs. 1,25,000
Share of Suman : Manu : Amandeep
= 50,000 × 12 : 75,000 × 9 : 1,25,000 × 6 = 6,00,000 : 6,75,000 : 7,50,000
= 600 : 675 : 750 = 8 : 9 : 10
Total profit = Rs. 99,495
Profit of Amandeep =  × 99,495 =  × 99,495 = Rs. 36,850

Let number of students of Grade 7 in auditorium A = 5a
Thus, number of students of Grade 8 in auditorium A = 4a
Let number of students of Grade 7 in auditorium B = 17b
Thus, number of students of Grade 8 in auditorium B = 3b
Total number of students of Grade 8 = 4a + 3b
Total number of students of Grade 7 = 17b + 5a
Now, (4a + 3b)/(17b + 5a) = 5/7
Or, a = (64/3)b
Let b = 3c
We get a = 64c
Total number of students in auditorium A = 9a = 576c
Total number of students in auditorium B = 20b = 60c
Required ratio = 576 : 60 = 48 : 5
Hence, answer option 4 is correct.

Let the total number of coins = x
Total number of 25 coins = 132
The ratio of 25 p, 50 p and Re 1 coins is 11 : 6 : 13.
So, 25 p coins = x  
132 = x  
x =  = 360
So, the total number of coins = 360
Total 50 p coins = 360  = 72
Total 1 Re coins = 360  = 156
Number of 25 p coins with second person = 132  = 48
Number of 50 p coins with second person = 72   = 12
Number of 1 Re coins with second person = 156   = 24
That is, the second person have 48 coins of 25 p, 12 coins of 50 p and 24 coins of 1 Re.
Total money = 48 x 0.25 + 12  0.50 + 24  1 = 12 + 6 + 24 = Rs. 42

Diminishing speed 
Let speed be S₁ when no stones are attached.
S₁ = 24
Let S₂ be the speed when stones are attached (where N be the number of stones)
S₂ = 24 -  (where k is proportionality constant)
According to given condition;
20 = 24 - 
2k = 4
k = 2
S₂ = 24 - 
For S₂ = 0 , we have

N = 144
It means that if we tie 144 stones, the balloon cannot go up in the air.
So, the highest number of stones that can be attached with the balloon is 143.

Let the total profit be Rs. x.
After donating 20% profit to old age home, remaining profit = 0.8x.
Out of the remaining profit, 50% is reinvested.
So, the remaining profit = 0.4x
Now this 0.4x has to be divided in the ratio 7 : 6.
Tanya's share = 0.4x × 
Sanya's share = 0.4x × 
Difference = 0.4x × – 0.4x ×  = 4400
= 0.4x ×= 4400
x = = Rs. 1,43,000

Total investment made by Akbar = 10,000 × 3 + 9,000 × 2 + 8,000 × 7
= 30,000 + 18,000 + 56,000 = 1,04,000
Total investment made by Birbal = 25,000 × 9 + 32,000 × 3
= 2,25,000 + 96,000 = 3,21,000
Total investment made by Tansen = P × 12
Total profit = 12,400
Share of Tansen in total profit
= 
2,400 = 
2,400 × 4,25,000 + 2,400 × 12P = 12,400 × 12P
2,400 × 4,25,000 = 10,000 × 12P
P =  = 8,500
So, initial investment made by Tansen = Rs. 8,500

Since, in between 12 and 1, the speed of minutes hand is similar to that of an ordinary clock, it take 5 minutes to cover first division.
Then its speed will become twice, because, the hand is between 1 and 2.
So, it takes  minutes. Between 2 and 3, the speed becomes thrice and takes  minutes.
So, in total it takes  minutes to reach 6 (9 : 30 am).
= 5 =  minutes = 12¼ minutes.
So, ordinary clock shows 9 hours 12 minutes 15 seconds.

Amount deposited by Harpreet and Gagan = Rs. 72,000
Amounts are in the ratio 7 : 9.
Let common ratio = x
Money deposited by Harpreet = 7x
Money deposited by Gagan = 9x
Now, 7x + 9x = Rs. 72,000
16x = Rs. 72,000
x = Rs. 4500
Money deposited by Harpreet = 4500 × 7 = Rs. 31,500
Money deposited by Gagan = 4500 × 9 = Rs. 40,500
Money left with Harpreet after withdrawal of Rs. 7500 = 31,500 - 7500 = Rs. 24,000
Ratio of amounts of Harpreet and Gagan is 4 : 5.
So, amount of Gagan = 5/4 × 24,000 = Rs. 30,000
Amount withdrawn by Gagan = 40,500 - 30,000 = Rs. 10,500