The ratio is the comparison of two values expressed as a quotient.
a : b = a/b
Problem 1:
Divide :
a) $50 in the ratio 1 : 4
b) $35 in the ratio 3 : 4
Solution :
a) We divide the given quantity 50 in the ratio 1 : 4.
Let the first part be x and the second part be 4x.
x + 4x = 50
5x = 50
x = 50/5 ==> 10
1x = 10
4x = 4(10) ==> 40
So, the denominations are 10 and 40 respectively.
b) Let the first and second parts e 3x and 4x respectively.
3x + 4x = 35
7x = 35
x = 35/7
x = 5
3x = 3(5) ==> 15
4x = 4(5) ==> 20
So, the denominations are $15 and $20.
Problem 2 :
A fortune of $800000 is to be divided in the ratio 3 : 7. What is the larger share?
Solution :
Let take first part to be 3x and second part to be 7x.
3x + 7x = 800000
10x = 800000
x = 800000/10
x = 80000
3x = 3(80000) ==> 240000
7x = 7(80000) ==> 560000
So, the largest share is $560000.
Problem 3 :
The ratio of girls to boys in a tennis club is 4 : 5. If there are 144 children in the club, how many are girls?
Solution :
Number of girls = 4x and boys = 5x
4x + 5x = 144
9x = 144
x = 144/9
x = 16
Girls 4x = 4(16)
= 64
So, there are 64 girls in the tennis club.
Problem 4 :
A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
Solution :
Ratio between alcohol to water in the first glass = 1 : 4
Let x be the capacity of the glass.
Quantity of alcohol in 1^{st} glass = x/5
Quantity of water in 1^{st} glass = 4x/5
Ratio between alcohol to water in the second glass = 2 : 3
Quantity of alcohol in 2^{nd} glass = 2x/5
Quantity of water in 2^{nd} glass = 3x/5
Problem 5 :
One full glass contains vinegar and water in the ratio 1 : 3. Another glass with twice the capacity of the first has vinegar and water in the ratio 1 : 4. If the contents of both glasses are mixed together, what is the ratio of vinegar to water?
Solution :
Let first glass capacity = x
In first glass,
Ratio of vinegar : water = 1 : 3
Second glass capacity = 2x
Vinegar = 1/5 (2x) = 2x/5
Water = 4/5 (2x) = 8x/5
Both glasses capacity = x + 2x = 3x
Vinegar = x/4 + 2x/5
Vinegar = 13x/20
Water = 3x/4 + 8x/5
Water = 47x/20
Ratio of vinegar to water = 13x/20: 47x/20
= 13: 47
Problem 6:
A lemon drink is mixed using one part lemon juice to seven parts water. If 250 ml of lemon juice is used, how much water should be added?
Solution :
Ratio between lemon juice to water = 1 : 7
Quantity o lemon juice = x
Quantity of water = 7x
here x = 250
quantity of water used = 250 (7)
= 1750
So, 1750 parts water should be added.
Problem 7:
At a Falcons vs Crocs basketball match, the ratio of supporters is 5: 3. If there are 4000 in the crowd, how many are Falcons supporters?
Solution :
The ratio of Falcons vs Crocs supporters = 5: 3
Falcons supporters = 5x
Crocs supporters = 3x
5x + 3x = 4000
8x = 4000
x = 4000/8
x = 500
Falcons supporters = 5x
= 5(500)
= 2500
So, 2500 Falcons supporters are in the basketball match.
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