Introduction to ratio problems with solutions.
Two values can be compared by (i) Subtraction (ii) Division.
If the weights of two quantities A and B are given by 8 kg and 32kg, then the weight of B is 32 – 8 = 24 kg more than the weight of A.
Also `32 / 8` = 4. The weight of B is in 4 times the weight of A.
Therefore, ratio is a relationship between two quantities which expresses how many times one quantity is of the other.
The ratio of two quantities x and y can be expressed as follows:
(i) as a fraction `x / y` .
(ii) as a division x ÷ y
(iii) also as x : y
The ratio can be obtained by dividing the first quantity by the second quantity.
Now let us see few problems on this topic ratio problems with solutions.
Example Problems on Ratio Problems with Solutions.
Ex 1: A plot is 100 m long and 20 m wide. Find the ratio between the following:
(i) Wide and length
(ii) Length and perimeter
Soln: Here wide = 40m, Length = 100 m
Therefore perimeter = 2 (wide + length)
= 2 (40 + 100) = 280 m.
(i) The ratio of wide and length = `40 / 100` = `2 / 5`
Therefore the ratio is 2 : 5.
(ii) The ratio of length and perimeter = `100 / 280` = `5 / 14` .
Therefore the ratio is 5 : 14.
Ex 2: Paul secured 45 marks out of 50 in English and 25 out of 30 in French. In which subject did he perform better?
Soln: Let us find the ratios of the marks.
In English, it is `45 / 50` = `9 / 10` `=>` 9 : 10
In French, it is `25 / 30` = `5 / 6` `=>` 5 : 6.
Hence Paul performed well in English as 9 : 10 is greater than 5 : 6
I like to share this How to do Ratios with you all through my article.
More Example Problems on Ratio Problems with Solutions.
Ex 3: Divide 1250 dollars between two persons in the ratio 12 : 13.
Soln: Here the total ratio is 12 + 12 = 25.
Therefore the value of 1 ratio = `1250 / 25` = 50
Therefore two persons will get 12 * 50 = 600 dollars and 13 * 50 = 650 dollars.
Ex 4: Two numbers are in the ratio 2 : 7. If the second number is 378, find the first number.
Soln: Given: `(First number) / 378` = `2 / 7` `=>` First number = `2 / 7 xx 378` = 108
Therefore the first number is 108.
Two values can be compared by (i) Subtraction (ii) Division.
If the weights of two quantities A and B are given by 8 kg and 32kg, then the weight of B is 32 – 8 = 24 kg more than the weight of A.
Also `32 / 8` = 4. The weight of B is in 4 times the weight of A.
Therefore, ratio is a relationship between two quantities which expresses how many times one quantity is of the other.
The ratio of two quantities x and y can be expressed as follows:
(i) as a fraction `x / y` .
(ii) as a division x ÷ y
(iii) also as x : y
The ratio can be obtained by dividing the first quantity by the second quantity.
Now let us see few problems on this topic ratio problems with solutions.
Example Problems on Ratio Problems with Solutions.
Ex 1: A plot is 100 m long and 20 m wide. Find the ratio between the following:
(i) Wide and length
(ii) Length and perimeter
Soln: Here wide = 40m, Length = 100 m
Therefore perimeter = 2 (wide + length)
= 2 (40 + 100) = 280 m.
(i) The ratio of wide and length = `40 / 100` = `2 / 5`
Therefore the ratio is 2 : 5.
(ii) The ratio of length and perimeter = `100 / 280` = `5 / 14` .
Therefore the ratio is 5 : 14.
Ex 2: Paul secured 45 marks out of 50 in English and 25 out of 30 in French. In which subject did he perform better?
Soln: Let us find the ratios of the marks.
In English, it is `45 / 50` = `9 / 10` `=>` 9 : 10
In French, it is `25 / 30` = `5 / 6` `=>` 5 : 6.
Hence Paul performed well in English as 9 : 10 is greater than 5 : 6
I like to share this How to do Ratios with you all through my article.
More Example Problems on Ratio Problems with Solutions.
Ex 3: Divide 1250 dollars between two persons in the ratio 12 : 13.
Soln: Here the total ratio is 12 + 12 = 25.
Therefore the value of 1 ratio = `1250 / 25` = 50
Therefore two persons will get 12 * 50 = 600 dollars and 13 * 50 = 650 dollars.
Ex 4: Two numbers are in the ratio 2 : 7. If the second number is 378, find the first number.
Soln: Given: `(First number) / 378` = `2 / 7` `=>` First number = `2 / 7 xx 378` = 108
Therefore the first number is 108.
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