Ratio and Proportion problems
- 1. If 4a = 5b and 7b = 9c, then a : b : c is equal to
Options- A. 45 : 36 : 28
- B. 44 : 33 : 28
- C. 28 : 36 : 45
- D. 36 : 28 : 45 Discuss
Correct Answer: 45 : 36 : 28
Explanation:
Given that 4a = 5b
? a/b = 5/4
Also 7b = 9c
? b/c = 9/7
? a : b = 5 : 4 = (5 x 9) : (4 x 9) = 45 : 36
and b : c = 9 : 7 = (9 x 4) : (7 x 4) = 36 : 28
? a : b : c = 45 : 36 : 28
- 2. If a/7 = b/9 = c/11, then find a : b : c?
Options- A. 11 : 9 : 7
- B. 9 : 7 : 11
- C. 7 : 9 : 11
- D. 11 : 7 : 9 Discuss
Correct Answer: 7 : 9 : 11
Explanation:
Let a/7 = b/9 = c/11 = K
Then, a = 7K, b = 9K, c = 11K
? a : b : c = 7K : 9K : 11K = 7 : 9 : 11
- 3. If 30% of A = 20 % of B, then find the value of A : B?
Options- A. 1 : 3
- B. 3 : 2
- C. 3 : 1
- D. 2 : 3 Discuss
Correct Answer: 2 : 3
Explanation:
Given that, 30 % of A = 20 % of B
? A/B = 20/30 = 2/3
? A : B = 2 : 3
- 4. If P : Q : R = 2 : 3 : 4, then find P/Q : Q/R : R/P?
Options- A. 8 : 9 : 24
- B. 9 : 8 : 24
- C. 24 : 8 : 9
- D. 8 : 24 : 9 Discuss
Correct Answer: 8 : 9 : 24
Explanation:
Given that, P : Q : R = 2 : 3 : 4
Let P = 2K, Q = 3K, R = 4K
? P/Q = 2K/3K = 2/3,
Q/R = 3K/4K = 3/4,
R/P = 4K/2K = 2/1
? P/Q : Q/R : R/P = 2/3 : 3/4 : 2/1
= (2 x 12)/3 : (3 x 12)/ 4 : (2 x 12)/1
= (2 x 4) : (3 x 3) : 24
= 8 : 9 : 24
- 5. If A = B/4 and B = C/2, then find the value of A : B : C?
Options- A. 8 : 4 : 1
- B. 4 : 2 : 1
- C. 1 : 4 : 8
- D. 1 : 2 : 4 Discuss
Correct Answer: 1 : 4 : 8
Explanation:
Given that, A = B/4
? A/B = 1/4 or A : B = 1 : 4
Also, B = C/2 or B/C = 1/2 or B : C = 1 :2
Now, we have A : B = 1 : 4; B : C = 1 : 2
A : B : C = ( 1 x 1 ) : ( 1 x 4 ) : ( 2 x 4 )
= 1 : 4 : 8
- 6. If 0.8 x A = 0.09 x B, then find A : B.
Options- A. 9 : 80
- B. 3 : 80
- C. 80 : 9
- D. 7 : 80 Discuss
Correct Answer: 9 : 80
Explanation:
Given that 0.8 x A = 0.09 x B
? A/B = 0.09/0.8 = 9/80
? A : B = 9 :80
- 7. If 1/x : 1/y : 1/z = 2 : 3 : 5, then determine x : y : z .
Options- A. 6 : 15 : 10
- B. 3 : 15 : 10
- C. 15 : 3 : 10
- D. 15 : 10 : 6 Discuss
Correct Answer: 15 : 10 : 6
Explanation:
Let 1/x = 2K, 1/y = 3K and 1/z = 5K
Then, x = K/2, Y = K/3 and z = K/5
? x : y : z = K/2 : K/3 : K/4
= 1/2 : 1/3 : 1/5
= 15 : 10 : 6
- 8. If a/3 = b/8, then ( a + 3 ) : ( b + 8 ) is equal to?
Options- A. 3 : 8
- B. 8 : 3
- C. 5 : 8
- D. 3 : 5 Discuss
Correct Answer: 3 : 8
Explanation:
Let a/3 = b/8 = K
Then, a = 3K, b = 8K
? (a + 3) / (b + 8) = (3K + 3) / (8K + 8)
= [3( K + 1)] / [8(K+1)] = 3/8
? ( a + 3 ) : (b + 8) = 3 : 8
- 9. If 1/2 of A = 2/5 of B = 1/3 of C, then A : B : C is equal to?
Options- A. 4 : 5 : 6
- B. 6 : 4 : 5
- C. 5 : 4 : 6
- D. 4 : 6 : 5 Discuss
Correct Answer: 4 : 5 : 6
Explanation:
1/2 of A = 2/5 of B = 1/3 of C
1/2 x A = 2/5 x B = 1/3 x C
Let A/2 = 2B/5 = C/3 = K
Then, A = 2K, B = 5K/2, C = 3K
? A: B : C = 2k : 5k/2 : 3k
? A: B : C = 4 : 5 : 6
- 10. If xy =36, then which of the following is correct?
Options- A. x : 9 = 4 : y
- B. 9 : x = 4 : y
- C. x :17 = y : 7
- D. x : 6 = y : 6 Discuss
Correct Answer: x : 9 = 4 : y
Explanation:
xy =36
? xy = 4 x 9,
? x/9 = 4/y
? x : 9 = 4 : y
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