Ratio and Proportion problems
- 1. Out of two sections A and B, 10 students of section B shift to A, as a result strength of A becomes 3 times the strength of B. But , if 10 students shift over from A to B, both A and B become equal in strength. Ratio of the number of students in section A that of section B is?
Options- A. 2 : 1
- B. 5 : 3
- C. 3 : 1
- D. 9 : 4 Discuss
Correct Answer: 2 : 1
Explanation:
A +10 = 3(B - 10)
? A - 3B = -20 ....(i)
And ( A - 10) = (B + 10)
? A - B = 20 ...(ii)
on subtracting Eq.(ii) from Eq.(i), we get
(A - 3B) - (A - B) = -20 - 20
? - 2B = - 40
there4; B = 20
Now, by using Eq. ...(ii),
there4; Ratio of the numbers of students of A and B = 40 : 20 = 2 : 1
- 2. A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got ? 2100 less than P, then how much amount did Q receive?
Options- A. ? 2500
- B. ? 2000
- C. ? 1500
- D. Couldn't be determined Discuss
Correct Answer: Couldn't be determined
Explanation:
Couldn't be determined, since the total amount of money is not given in either of the case
- 3. Nandita scores 80% marks in five subjects together, viz., Hindi, Science, Mathematics, English and Sanskrit, where in the maximum marks of each subject were 105, How many marks did Nandita score in Science, if she scored 89 marks in Hindi, 92 marks in Sanskrit, 98 marks in Mathematics and 81 marks in English?
Options- A. 60
- B. 75
- C. 65
- D. 70 Discuss
Correct Answer: 60
Explanation:
Total of maximum marks of all subjects = 105 x 5 = 525
Total marks obtained by Nandita = 80% of 525 = 525 x 80/100 = 420
Obtained marks of four subjects (Hindi, Sanskrit, Mathematics and English)
= 89 + 92 + 98 + 81 = 360
So, the obtained marks in Science = 420 - 360 = 60
- 4. Number of employees in a factory decreases in the ratio of 8 : 7 and salary of employees increases in the ratio of 5 : 6 . Find whether the total salary given to the employee is increasing or decreased and in What ratio?
Options- A. 19 : 20 increased
- B. 20 : 19 decreased
- C. None of above
- D. 21 : 20 decreased Discuss
Correct Answer: None of above
Explanation:
Let total number of employees in beginning = 8K and total number of employees in present = 7K
Let salary of an employee in beginning = 5L and salary of an employee in present = 6L
? Total salary in beginning = 8K x 5L = 40KL
and total salary in present = 7K x 6L = 42 KL
Required ratio = 40KL : 42KL = 20 : 21
Clearly, salary is increased.
- 5. Out of 120 applications for a post, 70 are males and 80 have a driver's licences . What is the ratio between the minimum to maximum number number of males having driver's license?
Options- A. 1 : 3
- B. 2 : 3
- C. 3 : 7
- D. 5 : 7 Discuss
Correct Answer: 3 : 7
Explanation:
Since there are 70 males out of 120 applicants, there must be 50 females out must have For the minimum number of males to have a driver's licence all 50 females must have a driver's license Thus the number of males having a driver's licence will be 80 - 50 = 30. The maximum possible number of males having a driver's license is 70. The ratio between the minimum and the maximum is 30 : 70 or 3 : 7 .
- 6. in a mixture of 60 L the ratio of acid and water is 2 : 1. If the ratio of acid and water is to be 1 : 2, then the amount of water (in liters) to be added to the mixture is?
Options- A. 55
- B. 60
- C. 50
- D. 45 Discuss
Correct Answer: 60
Explanation:
Quantity of acid in the mixture = (2/3) x 60 = 40 L
Quantity of water in the mixture = (1/3) x 60= 20 L
Let the required quantity of water be x L.
According to the question,
40/(20+ x) = 1/2
? 80 = 20 + x
? x = 60 L
- 7. Tea worth ? 126 kg and ? 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . If the mixture is worth ? 153 per kg, the price of the third variety per kg will be?
Options- A. ? 169.5
- B. ? 170.0
- C. ? 175.5
- D. ? 180.0 Discuss
Correct Answer: ? 175.5
Explanation:
Let the cost of third variety tea will be ? N per kg
According to the question,
(126 + 135 + 2N)/4 = 153
? (261 + 2N) = 4 x 153
? 2N = 612 - 261 = 351
? N = 351/2 = 175.50
? N = ? 175.5
Hence, the cost of third variety tea is ? 175.50 per kg .
- 8. Find the compound ratio of 2 : 7, 5 : 3 and 4 : 7?
Options- A. 147 : 40
- B. 40 : 147
- C. 147 : 30
- D. 30 : 147 Discuss
Correct Answer: 40 : 147
Explanation:
Required compound ratio = (2 x 5 x 4) / (7 x 3 x 7)
= 40/147
= 40 : 147
- 9. If A : B = 3 : 4 and B : C = 8 : 9 then find the value of A : B : C?
Options- A. 3 : 4 : 5
- B. 1 : 2 : 3
- C. 7 : 12 : 17
- D. 6 : 8 : 9 Discuss
Correct Answer: 6 : 8 : 9
Explanation:
Given that
A : B = 3 : 4 = ( 3 x 2 ) : (4 x 2 ) = 6 : 8
B : C = 8 : 9
? A : B : C = 6 : 8 : 9
As consequent of the first ratio is equal to the antecedent of second ratio.
- 10. If (a + b ) : (a - b) = 5 : 3, then find ( a 2 + b 2 ) : ( a 2 - b 2 ) .
Options- A. 17 : 15
- B. 25 : 9
- C. 4 : 1
- D. 16 : 1 Discuss
Correct Answer: 17 : 15
Explanation:
(a + b) / (a - b) = 5/3
? 3a + 3b = 5a - 5b
? 2a = 8b
? a = 4b,
? a/b = 4/1
Now, ( a2 + b2 ) / (a2 - b2 ) = [a2 / (b2+1)] / [a2 / (b2 -1)]
= [( a/b )2 + 1] / [( a/b )2 - 1] = [( 4/1 )2 + 1] / [( 4/1 )2 - 1]
= [16 + 1] / [16 - 1] = 17/15
? ( a2 + b2 ) : ( a2 - b2 ) = 17 : 15
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