Ratio, Proportion
- The sum of the squares of two positive numbers is greater than their product by 2 8 . If the ratio of the numbers 2 : 3 , find th e numbers .
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Let the numbers be 2x and 3x.
∴ (3x)2 + (2x)2 2 – 2x × 3x = 28
⇒ 13x2 – 6x2 = 28
⇒ 7x2 = 28⇒ x2 = 28 ; 4 7
⇒ x = √4 = 2
∴ Numbers are : 4 and 6Correct Option: A
Let the numbers be 2x and 3x.
∴ (3x)2 + (2x)2 2 – 2x × 3x = 28
⇒ 13x2 – 6x2 = 28
⇒ 7x2 = 28⇒ x2 = 28 ; 4 7
⇒ x = √4 = 2
∴ Numbers are : 4 and 6
- In an army selection process, the ratio of selected to unselected candidates was 4:1. If 90 less had applied and 20 less were selected, the ratio of selected to unselected candidates would have been 5:1. How many candidates had applied for the process ?
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Let the number of the selected candidates be 4x
Unselected candidates = x
According to the question,
Total new applicants = 5x – 90
Selected candidates = 4x – 20
Unselected candidates
= 5x – 90 – 4x + 20
= x – 70∴ 4x − 20 = 5 x − 70 1
⇒ 5x – 350 = 4x – 20
⇒ 5x – 4x = 350 – 20
⇒ x = 330
∴ Required number of total original applicants
= 5x = 5 × 330 = 1650Correct Option: A
Let the number of the selected candidates be 4x
Unselected candidates = x
According to the question,
Total new applicants = 5x – 90
Selected candidates = 4x – 20
Unselected candidates
= 5x – 90 – 4x + 20
= x – 70∴ 4x − 20 = 5 x − 70 1
⇒ 5x – 350 = 4x – 20
⇒ 5x – 4x = 350 – 20
⇒ x = 330
∴ Required number of total original applicants
= 5x = 5 × 330 = 1650
- In an army selection process, the ratio of selected to unselected candidates was 3 : 1. If 80 less had applied and 40 less selected, the ratio of selected to unselected candidates would have been 4 : 1. How many candidates had applied for the process?
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In selection process,
Selected candidates = 3x
Unselected candidates = x
According to the question,
In case II,
Total applicants = 4x – 80
Selected candidates = 3x – 40
Unselected candidates
= (4x – 80) – (3x – 40)
= 4x – 80 – 3x + 40
= x – 40∴ 3x − 40 = 4 x − 40 1
⇒ 4x – 160 = 3x – 40
⇒ 4x – 3x = 160 – 40
⇒ x = 120
∴ Required total applicants
= 4x = 4 × 120 = 480Correct Option: A
In selection process,
Selected candidates = 3x
Unselected candidates = x
According to the question,
In case II,
Total applicants = 4x – 80
Selected candidates = 3x – 40
Unselected candidates
= (4x – 80) – (3x – 40)
= 4x – 80 – 3x + 40
= x – 40∴ 3x − 40 = 4 x − 40 1
⇒ 4x – 160 = 3x – 40
⇒ 4x – 3x = 160 – 40
⇒ x = 120
∴ Required total applicants
= 4x = 4 × 120 = 480
- The rates of working of A and B are in the ratio of 2 : 3. The number of days taken by each of them to finish the work is in the ratio :
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Rate of working × 1 Time taken ∴ Ratio of days taken = 1 : 1 2 3
= 3 : 2Correct Option: C
Rate of working × 1 Time taken ∴ Ratio of days taken = 1 : 1 2 3
= 3 : 2
- A shopkeeper earns a profit of 15% after selling a book at 20% discount on the printed price. The ratio of the cost price and printed price of the book is :
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Let the C.P. of article be Rs. x and marked price be Rs. y.
According to the question,
80% of y = 115% of x⇒ y × 80 = x × 115 100 100
⇒ 80y = 115x⇒ x = 80 = 16 y 115 23 Correct Option: C
Let the C.P. of article be Rs. x and marked price be Rs. y.
According to the question,
80% of y = 115% of x⇒ y × 80 = x × 115 100 100
⇒ 80y = 115x⇒ x = 80 = 16 y 115 23
