Ratio and Proportion problems
- 1. 729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio of 7 :3?
Options- A. 60 ml
- B. 70 ml
- C. 81 ml
- D. 90 ml Discuss
Correct Answer: 81 ml
Explanation:
Milk = (729 x 7/9) = 567 ml
Water = (729 x 2/9) = 162 ml
Let water to be added is w
? 567 / (162 + w) = 7/3
? 3 x 567 - 7 x 162 = 7 x w
? 1701 - 1134 = 7 x w
? 7w = 1701 - 1134
? w = 567/7 = 81 ml
- 2. A and B are two alloys of gold and copper prepared by mixing metals in proportions 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to from a third alloy C, the proportion of gold and copper in C will be?
Options- A. 5 : 9
- B. 5 : 7
- C. 7 : 5
- D. 9 : 5 Discuss
Correct Answer: 7 : 5
Explanation:
Gold in C =(7/9 + 7/18) = 21/18 = 7/6
Copper in C = (2/9 + 11/18) = 15/18 = 5/6
? Gold : Copper = 7/6 : 5/6 = 7 : 5
- 3. Some money is divided among A, B and C in such a way that 5 times A's share 3 times B's share and 2 times C's share are all equal. the ratio between the share of A, B, C is?
Options- A. 5 : 3 : 2
- B. 2 : 2 : 5
- C. 15 : 10 : 6
- D. 6 : 10 : 15 Discuss
Correct Answer: 6 : 10 : 15
Explanation:
? 5A = 3B = 2C = x
? A = x/5, B=x/3 and C =x/2
? A : B : C = x/5 : x/3 : x/2 = 6 : 10 : 15
- 4. 94 is divided into two parts in such a way that fifth parts of the first and eighth parts of the second are in the ratio 3 : 4. The first parts is?
Options- A. 27
- B. 30
- C. 36
- D. 48 Discuss
Correct Answer: 30
Explanation:
? 1/5A : 1/8B = 3 : 4
? 8A/5B = 120/160
? A/B = 120/160 x 5/8 = 15/32
? First part = Rs. (94 x 15/47) = Rs. 30
- 5. Rs. 680 has been divided among A, B, C such that A gets 2/3 of what B gets 1/4 of what C gets. Then B's share is?
Options- A. Rs. 60
- B. Rs. 80
- C. Rs. 120
- D. Rs. 160 Discuss
Correct Answer: Rs. 120
Explanation:
Suppose C gets Re.1. Then B gets Re. (1/4)
? A gets = Re. (2/3 x 1/4) = Re. 1/6
? A : B : C = 1/6 : 1/4 : 1 = 2 : 3 : 12
Hence B's share = Rs. (680 x 3/17) = Rs. 120
- 6. Rs. 2430 has been divided among A , B, C in such a way their if their shares be diminished by Rs. 5, Rs.10 and Rs. 15 respectively. The remainders are in the ratio 3 : 4 : 5. Then A's share is?
Options- A. Rs . 800
- B. Rs. 600
- C. Rs. 595
- D. Rs. 605 Discuss
Correct Answer: Rs. 605
Explanation:
? Remainder = Rs. [ 2430 - (5 + 10 + 15)] = Rs. 2400
&there4 A's share = Rs. [ (2400 x 3/12) + 5 ] = Rs. 605
- 7. The sides of triangle are in the ratio 1/3 : 1/4 : 1/5 and its perimeter is 94 cm. the length of smallest side is?
Options- A. 18.8 cm
- B. 23.5 cm
- C. 24 cm
- D. 31.3 cm Discuss
Correct Answer: 24 cm
Explanation:
Ratio of sides 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Length of smallest side = 94 x (12/47) cm. = 24 cm.
- 8. Rs. 53 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is?
Options- A. 16 : 9 : 18
- B. 25 : 18 : 10
- C. 18 : 25 : 10
- D. 15 : 8 : 30 Discuss
Correct Answer: 25 : 18 : 10
Explanation:
Suppose C gets Rs. x
Then, B gets Rs. (x + 8) and A gets Rs. (x + 15)
? x + x + 8 + x + 15 = 53
? x =10
so, A : B : C = 25 : 18 : 10
- 9. A sum of money is divided among A, B, C so that to each rupee A gets, B gets 65 paise and C gets 35 paise. If C's share is Rs. 28, the sum is?
Options- A. Rs. 120
- B. Rs. 140
- C. Rs. 160
- D. Rs. 180 Discuss
Correct Answer: Rs. 160
Explanation:
A : B : C = 100 : 65 : 35 = 20 : 13 : 7
If C's share is Rs. 7, the sum is Rs. 40.
If C's share is Rs. 28, the sum is Rs.(40/7 x 28) = Rs. 160.
- 10. The incomes of A and B are in the ratio 3 : 2 and their expenditures in the ratio 5 : 3. If each saves Rs. 1,000. A's income is?
Options- A. Rs. 3000
- B. Rs. 4000
- C. Rs. 6000
- D. Rs. 9000 Discuss
Correct Answer: Rs. 6000
Explanation:
Let their incomes be 3x, 2x and expenditures 5y, 3y respectively.
Then, 3x - 5y = 1000 and 2x - 3y =1000.
Solving these equations we get x = 2000, y = 1000
? A's income = 3x = Rs.6000
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