## Ratio Questions and Answers Part-2

1.The ratio of water and milk in a 30 liter mixture is 7 : 3. Find the quantity of water to be added to the mixture in order to make this ratio 6 : 1.
a) 30
b) 32
c) 33
d) 35

Explanation: Here,Let water = 7x and milk = 3x
7x + 3x = 30
x = 3
So, water = 7x = 7 × 3 = 21 liter
Milk = 3x = 3 × 3 = 9 liter
Now, we keep milk constant and add water to mixture to get ratio 6 : 1
Let water in this mixture = 6y and milk = y
We have, milk = 9 liter, so y = 9 liter
Water = 6y = 6 × 9 = 54 liter
Then extra water to be added is 33 liter

2. The incomes of A and B are in the ratio 3 : 2 and their expenditure are in ratio 5 : 3. If each saves Rs. 1000, then, A's income can be:
a) Rs. 3000
b) Rs. 4000
c) Rs. 6000
d) Rs. 9000

Explanation: Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.
3x - 5y = 1000 ------- (i) × 3
2x - 3y = 1000 ---------- (ii) × 5
9x - 15y - 10x + 15y = 3000 - 5000
-x = -2000
x = 2000
Then, income of A = 3x = 3 × 2000 = Rs. 6000

3. The difference between two positive numbers is 10 and the ratio between them is 5 : 3. Find the product of the two numbers.
a) 375
b) 175
c) 275
d) 125

Explanation: Let the two positive numbers be 5x and 3x respectively
5x - 3x = 10
x = 5
Then numbers are 25 and 15
Thus, their product = 25 × 15 = 375

4. If 30 oxen can plough $$\frac{1}{7}$$ th of a field in 2 days, how many days 18 oxen will take to do the remaining work?
a) 30 days
b) 20 days
c) 15 days
d) 18 days

Explanation: We will use work equivalence method,
\eqalign{ & \frac{{30}}{{18}} = \frac{{ {\frac{1}{7}} }}{{ {\frac{6}{7}} }} \times \frac{x}{2} \cr & \frac{5}{3} = {\frac{1}{6}} \times \frac{x}{2} \cr & \,x = \frac{{60}}{3} = 20\,{\text{days}} \cr}

5. A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
a) 11 : 15
b) 15 : 11
c) 16 : 15
d) 15 : 16

Explanation: 3dog = 4 cat
$$\frac{{{\text{dog}}}}{{{\text{cat}}}} = \frac{4}{3}$$
Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter
Then, ratio of speed of cat and dog = $$\frac{{3 \times 5}}{{4 \times 4}}$$  = 15 : 16

6. Brindavan Express leave Chennai Central Station every day at 07.50 am and goes to Bangalore City Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1 : 4. The fare for this travel is in the ratio 3 : 1. The total fare collected was Rs. 224000. (Rs. Two lakhs twenty four thousand only). What was the fare collected from I class passengers on that day?
a) Rs. 32,000
b) Rs. 96,000
c) Rs.1,28,000
d) Rs. 5,00,000

Explanation: Let the number of passenger traveling by first class be x
Then, number of passenger traveling by second class will be 4x
But the fare is in the ratio 3 : 1
In other words, if 3y fare is collected per I class passenger, y would be collected per II class passenger
Fares of I class passengers : Fares of II class passengers
= x × 3y : 4x × y
= 3 : 4
If total fare is 3 + 4 = 7, then I class passengers should pay Rs. 3
Similarly, we can calculate the fare of I class passengers when total was 224000
 Total Fare Class Fare 7 3 224000 ?

= $$224000 \times \frac{3}{7}$$
= Rs. 96000

7. A vessel of capacity 2 litre has 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. what is the new concentration of mixture ?
a) 29%
b) 49%
c) 31%
d) 71%

Explanation: Amount of alcohol in first vessel,
= 25% of 2 litre
= 0.25 × 2 = 0.5 litre
Amount of alcohol in second vessel,
= 40% of 6 litre
= 0.4 × 6 = 2.4 litre
Total amount of alcohol out of 10 litres of mixture is
0.5 + 2.4 = 2.9 litre
Concentration of the mixture is,
$$\frac{{2.9 \times 100}}{{10}}$$
= 29%

8. The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?
a) 3 : 4
b) 2 : 3
c) 1 : 3
d) 2 : 1

Explanation: Let, B1 : B2 : B3 = 3x : 4x : 5x and
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
x = $$\frac{3y}{5}$$ and,
∴ 3x : 4x : 5x (putting the vale of x)
= $$\frac{{9{\text{y}}}}{5}:\frac{{{\text{12y}}}}{5}:\frac{{{\text{15y}}}}{5}$$
= 9y : 12y : 15y
5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y
Increment in first basket = 16
Increment in second basket = 8
Required ratio = $$\frac{{16}}{8}$$ = 2 : 1

9. At a casino in Mumbai, there are 3 tables A, B and C. The payoffs at A is 10 : 1, at B is 20 : 1 and C is 30 :1. If a man bets Rs. 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be ?
a) Rs. 4000
b) Rs. 4500
c) Rs. 2500
d) Rs. 2000

Explanation: Maximum earning will be only possible when he will won on the maximum yielding table
A → 10 : 1
B → 20 : 1
C → 30 : 1
i.e., he won B and C but lost on A
20 × 200 + 30 × 200 - 1 × 200 = 9800
Minimum earnings will be when he won on table A and B and lose on table 3
10 × 200 + 20 × 200 - 1 × 200 = 5800
Therefore, difference = 9800 - 5800 = Rs. 4000

10. A track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute. The ratio of their speeds is:
a) 4 : 3
b) 3 : 5
c) 3 : 4
d) 50 : 3

Speed of bus = $$\frac{{33\,{\text{kms}}}}{{45}}$$   = $$\frac{{33000}}{{45}}$$  = 733.33 m/minute
Ratio of their speeds = $$\frac{{550}}{{733.33}}$$  = 3 : 4