Ratio and Proportion problems
- 1. The total number of students in school is 2140. If the number of girls in the school is 1200, then what is the ratio of the total number of boy to the total number of girls in the school?
Options- A. 26 : 25
- B. 47 : 60
- C. 18 : 13
- D. 31 : 79 Discuss
Correct Answer: 47 : 60
Explanation:
Number of boy = ( 2140 - 1200 ) = 940
? Boys : Girls = 940 : 1200 = 47 : 60
- 2. The speed of three cars in the ratio of 2 : 3 : 4 Find the ratio between the time taken by these cars to cover the same distance?
Options- A. 2 : 3 : 4
- B. 4 : 3 : 2
- C. 4 : 3 : 6
- D. 6 : 4 : 3 Discuss
Correct Answer: 6 : 4 : 3
Explanation:
Ratio of Speed = 2 : 3 : 4
Ratio of time taken = (1/2) : (1/3) : (1/4) = 6 : 4 : 3
- 3. If P : Q : = 8 : 15 and Q : R = 3 : 2, then find P : Q : R
Options- A. 8 : 15 : 7
- B. 7 : 15 : 8
- C. 8 : 15 : 10
- D. 10 : 15 : 8 Discuss
Correct Answer: 8 : 15 : 10
Explanation:
Given that, P : Q = 8 : 15, Q : R = 3 : 2
P : Q : R = (8 x 3) : (15 x 3) : (15 x 2) = 24 : 45 : 30
? P : Q : R = 8 : 15 : 10
Here, consequent of first ratio should be equal to the antecedent of second ratio.
- 4. If P : Q = 8 : 15, Q : R = 5 : 8 and R : S = 4 : 5, then P : S is equal to
Options- A. 4 : 15
- B. 2 : 15
- C. 3 : 19
- D. 7 : 15 Discuss
Correct Answer: 4 : 15
Explanation:
Given, P/Q = 8/15, Q/R = 5/8, R/S = 4/5
? P/S = (P/Q) x (Q/R) x (R/S)
? P/S = (8/15) x (5/8) x (4/5) = 4/15
? P : S = 4 : 15
- 5. If A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10, then what is A : D equal to?
Options- A. 1 : 7
- B. 2 : 7
- C. 1 : 5
- D. 5 : 1 Discuss
Correct Answer: 1 : 7
Explanation:
Here, A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10
? A/D = (A/B) x (B/C) x (C/D)
= (2/3) x (5/7) x (3/10)
= 1/7
? A : D = 1 : 7
- 6. Calculate the 3rd proportional to 15 and 30.
Options- A. 55
- B. 15
- C. 65
- D. 60 Discuss
Correct Answer: 60
Explanation:
Let the 3rd proportional = k
Then, 15 : 30 : : 30 : k
? 15/30 = 30/k
? 15k = 30 x 30
? 15k = 30 x 30
? k = (30 x 30) / 15 = 60
- 7. Find the mean proportional between 9 and 64.
Options- A. 25
- B. 24
- C. 27
- D. 35 Discuss
Correct Answer: 24
Explanation:
Required mean proportional = ?9 x 64
= 3 x 8 = 24
- 8. If P 2 + 4Q 2 = 4PQ, then determine P : Q.
Options- A. 1 : 3
- B. 3 : 1
- C. 2 : 1
- D. 1 : 2 Discuss
Correct Answer: 2 : 1
Explanation:
P2 + 4Q2 = 4PQ
? P2 + 4Q2 - 4PQ = 0
? (P - 2Q)2 = 0
? P - 2Q = 0
? P = 2Q
? P/Q = 2/1
? P : Q = 2 : 1
- 9. If P : Q = 7 : 5, then what is the value of (5P - 2Q) : (3P + 2Q)?
Options- A. 5/4
- B. 6/5
- C. 25/31
- D. 31/42 Discuss
Correct Answer: 25/31
Explanation:
Given, P/Q = 7/5
? (5P - 2Q) / (3P + 2Q) = (5 x 7 - 2 x 5) / (3 x 7 + 2 x 5)
= (35 - 10) / (21 + 10)
= 25/31
- 10. Two number are in the ratio of 4 : 7. If 5 is subtracted from each, the ratio becomes 1 : 2. Find the greater number.
Options- A. 15
- B. 40
- C. 20
- D. 35 Discuss
Correct Answer: 35
Explanation:
Let 1st number be 4k and 2nd number be 7k.
According to the question,
(4k - 5) / (7k - 5) = 1/2
? 8k - 10 = 7k - 5
? 8k - 7k = 10 - 5
? k = 5
? Greater number = 7k = 7 x 5 = 35
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