Ratio and Proportion problems
- 1. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are?
Options- A. 3, 5
- B. 7, 9
- C. 13, 22
- D. 15, 25 Discuss
Correct Answer: 15, 25
Explanation:
Let the number be 3a and 5a
Then, (3a + 10) / (5a + 10) = 5/7
? 7(3a + 10) = 5 x (5a + 10)
? 4a = 20
? a = 5
So, the number are 15, 25.
- 2. The ratio between Sumit's and Prakash's age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit's age to Prakash's age after 6 years will be?
Options- A. 1 : 2
- B. 2 : 3
- C. 3 : 4
- D. 3 : 8 Discuss
Correct Answer: 3 : 4
Explanation:
Let their ages be 2x and 3x years.
? 3x - 2x = 6
? x = 6
? Sumit's age = 12 years, Prakash's age = 18 years
After 6 years, Sumit's age = 18 years
After 6 Years, prakash's age = 24 years
? Required ratio of their ages = 18 : 24 = 3 : 4
- 3. The ages of Vivek and Sumit are in the ratio 2 : 3. After 12 years, their ages wiil be in the ratio 11:15. The age of Sumit is?
Options- A. 32 years
- B. 42 years
- C. 48 years
- D. 56 years Discuss
Correct Answer: 48 years
Explanation:
Let their ages be 2x and 3x years
(2x + 12) / (3x + 12) = 11 /15
? 15(2x + 12) = 11(3x + 12)
? 3x = 48
? x = 16
? age of sumit = 3x = 48 years
- 4. The ratio of father's age to son's age is 4 : 1. The product of their age is 196. The ratio of their ages after 5 years will be?
Options- A. 3 : 1
- B. 10 : 3
- C. 11 : 4
- D. 14 : 5 Discuss
Correct Answer: 11 : 4
Explanation:
Let their ages be 4x and x years.
? 4x2 = 196
? x2 = 49
? x = 7
Their ages are 28 years and 7 years.
Ratio of their ages be after 5 years = 33 : 12 = 11 : 4.
- 5. The ratio between The ages of Kamla and Savitri is 6 : 5 and the sum of their age is 44 years.The ratio of their ages after 8 years wiil be?
Options- A. 5 : 6
- B. 7 : 8
- C. 8 : 7
- D. 14 : 13 Discuss
Correct Answer: 8 : 7
Explanation:
Let their ages be 4x and x years.
? 6x + 5x = 44
? x = 4
So their present ages are 24 years and 20 years
Ratio of their ages after 8 years = 32 : 28 = 8 : 7.
- 6. A father's age was 5 times his son's age 5 years ago, and will be 3 times son's age after 2 years the ratio of their present ages is?
Options- A. 5 : 2
- B. 5 : 3
- C. 10 : 3
- D. 11 : 5 Discuss
Correct Answer: 10 : 3
Explanation:
Let son's age 5 years ago = x years.
Then father's age at that time = 5x years.
After 2 years, son's age = (x + 7) years.
After 2 years, father's age = (5x + 5)
? 3(x + 7) = 5x + 7
? x = 7
Father's age now = ( 5x + 5 ) = 40 years
son's age now = (x+5) = 12 years
? Ratio of their present ages = 40 : 12 = 10 : 3
- 7. The average age of 3 girls is 20 years and their ages are in the proportion 3 : 5 : 7. the age of youngest girl is?
Options- A. 4 years
- B. 6 years 8 months
- C. 8 years 3 months
- D. 12 years Discuss
Correct Answer: 12 years
Explanation:
Their total age = (3 x 20) yeras = 60 years
Let their ages be 3x, 5x and 7x years.
Then 3x + 5x + 7x = 60
? x = 4
? yongest girl is = 3x = 12 years old.
- 8. A man has some hens and cows. If the number of heads be 48 and number of feet equal 140 the number of hens will be?
Options- A. 22
- B. 23
- C. 24
- D. 26 Discuss
Correct Answer: 26
Explanation:
Let the numbers of hens = x and number of cows = y
Then x + y = 48 and 2x + 4y = 140
Solving these equations, we get 2y = 44
? y = 22
So, x = (48 - 22) = 26
? Number of hens = 26.
- 9. 6 man, 8 woman, 6 children complete a job for a sum of Rs. 950. if their individuals wages are in ratio 4 : 3 : 2, the total money earned by the children is?
Options- A. Rs. 190
- B. Rs. 195
- C. Rs. 215
- D. Rs. 230 Discuss
Correct Answer: Rs. 190
Explanation:
Ratio of wages of 6 men, 8 women and 6 = (6 x 4) : (8 x 3) : (6 x 2) = 24: 24 : 12
= 2 : 2 : 1
? Total money earned by children = Rs. (950 x 1/5)
= Rs. 190
- 10. The ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is?
Options- A. 15
- B. 20
- C. 45
- D. 60 Discuss
Correct Answer: 45
Explanation:
Let the numbers be 3x and 4x
Then, their L.C.M. = 12x
? 12x = 180
? x = 15
Hence, the first number = 45
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