Ratio, Proportion
- The total marks obtained by Arun in English and Mathematics are 170. If the difference between his marks in these two subjects is 10, then the ratio of his marks in these subjects is
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According to the question,
E + M = 170 ....(i)
E – M = 10 ....(ii)
Adding both the equations,
2E = 180 ⇒ E = 90
From equation (i),
M = 170 – 90 = 80∴ E = 9 = 9 : 8 M 8 Correct Option: C
According to the question,
E + M = 170 ....(i)
E – M = 10 ....(ii)
Adding both the equations,
2E = 180 ⇒ E = 90
From equation (i),
M = 170 – 90 = 80∴ E = 9 = 9 : 8 M 8
- In a cricket match the total number of runs scored by Sachin, Vinod and Sourav is 285. The ratio of the number of runs scored by Sachin and Sourav is 3 : 2 and that of the runs scored by Sourav and Vinod is also 3 : 2. The number of runs scored by Sachin in that match is
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Sachin : Sourav = 3 : 2
Sourav : Vinod = 3 : 2
Ratio of the runs scored by Sachin, Sourav and Vinod respectively
= 3 × 3 : 2 × 3 : 2 × 2 = 9 : 6 : 4
∴ Runs scored by Sachin= 9 × 285 = 135 19 Correct Option: A
Sachin : Sourav = 3 : 2
Sourav : Vinod = 3 : 2
Ratio of the runs scored by Sachin, Sourav and Vinod respectively
= 3 × 3 : 2 × 3 : 2 × 2 = 9 : 6 : 4
∴ Runs scored by Sachin= 9 × 285 = 135 19
- In an examination, the number of those who passed and the number of those who failed were in the ratio 25 : 4. If five more had appeared and the number of failures was 2 less than earlier, the ratio of passers to failures would have been 22 : 3. The total number who appeared at the examination is
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Let the number of failures
= 4x and that of passers = 25 x
∴ Total number of students
= 4x + 25x = 29 x
In case II
Number of students = 29x + 5
Number of failures = 4 x – 2
∴ Number of passers
= 29x + 5 – 4x + 2 = 25x +7
∴ According to the question,25x + 7 = 22 4x − 2 3
⇒ 88x – 44 = 75x +21
⇒ 88x –75x = 44 +21
⇒ 13x = 65⇒ x = 65 = 5 13
∴ Total number of students
= 29x = 29 × 5 = 145Correct Option: A
Let the number of failures
= 4x and that of passers = 25 x
∴ Total number of students
= 4x + 25x = 29 x
In case II
Number of students = 29x + 5
Number of failures = 4 x – 2
∴ Number of passers
= 29x + 5 – 4x + 2 = 25x +7
∴ According to the question,25x + 7 = 22 4x − 2 3
⇒ 88x – 44 = 75x +21
⇒ 88x –75x = 44 +21
⇒ 13x = 65⇒ x = 65 = 5 13
∴ Total number of students
= 29x = 29 × 5 = 145
- In an innings of a cricket match, three players A, B and C scored a total of 361 runs. If the ratio of the number of runs scored by A to that scored by B and also number of runs scored by B to that scored by C be 3 : 2, the number of runs scored by A was
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A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
∴ A : B :C = 9 : 6 : 4
Total runs = 361∴ Number of runs scored by A = 9 × 361 (9 + 6 + 4) = 9 × 361 = 171 19 Correct Option: A
A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
∴ A : B :C = 9 : 6 : 4
Total runs = 361∴ Number of runs scored by A = 9 × 361 (9 + 6 + 4) = 9 × 361 = 171 19
- The ratio of the first and second class train fares between two stations is 3 : 1 and that of the numbers of passengers travelling between the two stations by first and second classes is 1 : 50. If on a particular day, ₹ 1, 325 are collected from passengers travelling between the two stations, then the amount collected from the second class passengers is
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Ratio of first and second class fares = 3 : 1
Ratio of number of passengers = 1 : 50
∴ Ratio of total amount
= 3 × 1 : 1 × 50 = 3 : 50
∴ Amount collected from second class passengers= ₹ 
50 × 1325 
= ₹ 1250 53 Correct Option: A
Ratio of first and second class fares = 3 : 1
Ratio of number of passengers = 1 : 50
∴ Ratio of total amount
= 3 × 1 : 1 × 50 = 3 : 50
∴ Amount collected from second class passengers= ₹ 50 × 1325 = ₹ 1250 53
