Ratio, Proportion
- In a school there were 1554 students and the ratio of the number of the boys and girls was 4 : 3. After a few days, 30 girls joined the school but a few boys left; as a result the ratio of the boys and girls became 7 : 6. The number of boys who left the school is
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In the school,
Boys ⇒ 4 × 1554 = 888 7 Girls ⇒ 3 × 1554 = 666 7
After 30 days,
Girls = 666 + 30 = 696
If x boys leave the school, then,
According to the question,888 − x = 7 696 6 ⇒ 888 − x = 7 116
⇒ 888 – x = 116 × 7 = 812
⇒ x = 888 – 812 = 76Correct Option: A
In the school,
Boys ⇒ 4 × 1554 = 888 7 Girls ⇒ 3 × 1554 = 666 7
After 30 days,
Girls = 666 + 30 = 696
If x boys leave the school, then,
According to the question,888 − x = 7 696 6 ⇒ 888 − x = 7 116
⇒ 888 – x = 116 × 7 = 812
⇒ x = 888 – 812 = 76
- In a 500 metre race, the ratio of speeds of two runners P and Q is 3 : 5. P has a start of 200 metre then the distance between P and Q at the finish of the race is
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Time taken by P in covering 300 metre
= 300 = 100 seconds 3
Distance covered by Q in 100 seconds
= 5 × 100 = 500 metre
So, both reach at the same time.
Correct Option: B
Time taken by P in covering 300 metre
= 300 = 100 seconds 3
Distance covered by Q in 100 seconds
= 5 × 100 = 500 metre
So, both reach at the same time.
- In a library the ratio of story books and other books is 7 : 2 and there are 1512 story books. Due the collection of some more story books the said ratio becomes 15 : 4. The number of story books collected is
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Story books ⇒ 1512
Other books ⇒ 2 × 1512 = 432 7
Additional story books = x∴ 1512 + x = 15 432 4
⇒ 6048 + 4x = 432 × 15 = 6480
⇒ 4x = 6480 – 6048 = 432⇒ x = 432 = 108 4 Correct Option: A
Story books ⇒ 1512
Other books ⇒ 2 × 1512 = 432 7
Additional story books = x∴ 1512 + x = 15 432 4
⇒ 6048 + 4x = 432 × 15 = 6480
⇒ 4x = 6480 – 6048 = 432⇒ x = 432 = 108 4
- Tom is chasing Jerry. In the same interval of time Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 jumps is equal to the distance covered by Jerry in 5 jumps. The ratio of speed of Tom and Jerry is
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7 jumps of Tom ≡ 5 jumps of Jerry
∴ 8 jumps of Tom ≡ 5 × 8 7 ∴ Required ratio = 40 : 6 7
= 40 : 42 = 20 : 21Correct Option: D
7 jumps of Tom ≡ 5 jumps of Jerry
∴ 8 jumps of Tom ≡ 5 × 8 7 ∴ Required ratio = 40 : 6 7
= 40 : 42 = 20 : 21
- A got twice as many marks in English as in Science. His total marks in English, Science and Mathematics is 180. If the ratio of his marks in English and Mathematics is 2 : 3, what is his marks in Science ?
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Marks obtained by A in English = 2x (let)
Marks obtained in Maths = 3x
Marks obtained in Science = x
According to the question,
2x + 3x + x = 180
⇒ 6x = 180⇒ x = 180 = 30 6
= Marks obtained in scienceCorrect Option: C
Marks obtained by A in English = 2x (let)
Marks obtained in Maths = 3x
Marks obtained in Science = x
According to the question,
2x + 3x + x = 180
⇒ 6x = 180⇒ x = 180 = 30 6
= Marks obtained in science
