Ratio and Proportion problems
- 1. If 6 men and 3 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time ?
Options- A. 1 : 2
- B. 2 : 1
- C. 3 : 1
- D. 1 : 3 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1 : 2
Explanation:
6M + 3B = 4(1M + 1B)
6M + 3B = 4M + 4B
2M = 1B
M/B = 1/2
- 2. The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is:
Options- A. 10
- B. 15
- C. 20
- D. 30 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 30
Explanation:
Let the three parts M, N, O.
Then, M:N = 2:3 and N:O = 5:8
= (5 x 3/5) : (8 x 3/5) = 3:24/5
M:N:O = 2:3:24/5
= 10:15:24 => N = 98 x 15/49 = 30.
- 3. 80 litres of diesel is required to travel 800 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 1000 kms using 1200 cc engine ?
Options- A. 120 lit
- B. 140 lit
- C. 110 lit
- D. 150 lit Also asked in: Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 150 lit
Explanation:
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 80 litres.
=> the amount of diesel required to cover a distance of 1000 kms = 1000 x 80/800 = 100 litres
However, the vehicle uses a 1200 cc engine and it is given that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800 x 100 = 150 litres.
- 4. The ratio of the angles of a triangle is 3 : 4 : 5. The three angles of a quadrilateral is equal to three angles of this triangle. What is the sum of the largest angle and second smallest angle of the quadrilateral ?
Options- A. 225 deg
- B. 210 deg
- C. 205 deg
- D. 245 deg Also asked in: CAT, GATE, Bank Clerk, Bank PO, AIEEE, Bank Exams
Correct Answer: 225 deg
Explanation:
Angle of triangle = 180 × 3/12
= 45 deg
Other angles of the triangle are = 60 deg, 75 deg
Angle of quadrilateral
= 360 - (45 + 60 + 75)
= 180 deg
Therefore, the four angles of the quadrilateral are 45, 60, 75 & 180 degrees.
Hence, the sum of largest and smallest angle of the quadrilateral are 180 + 45 = 225 deg.
- 5. In Maa Yatri Temple every devotee offers fruits to the orphans. Thus every orphan receives bananas, oranges and grapes in the ratio of 3:2:7 in terms of dozens. But the weight of a grape is 24 gm and weight of a banana and an orange are in the ratio of 4:5, while the weight of an orangeis 150gm. Find the ratio of all the three fruits in terms of weight, that an orphan gets
Options- A. 90:75:42
- B. 180:150:82
- C. 75:42:90
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Ratio of fruits (by dozen) = 3:2:7
Ratio of fruits (by weight) = 120 :150: 24
Therefore, Ratio of fruits (combined) by weight = 3 x 120 : 2 x 150 : 7 x 24 = 30 : 25 : 14
- 6. Out of 135 applicants for a post, 60 are graduates and 80 have experience. What is the ratio of minimum to maximum number of graduates having experience?
Options- A. 12:1
- B. 5:1
- C. 1:5
- D. 1:12 Also asked in: Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 1:12
Explanation:
Given total applicants = 135
Given graduates are G=60
Otherthan graduates=135-60 = 75
Given experienced candidates = 80
1) For maximum number of graduates have experience
Total graduates to have experience = 60
2) For minimum number of graduates have experience
Remaining after taking other than graduates in experience= 80-75 = 5
- 7. Salaries of Karthik, Arun and Akhil were in the ratio 4 : 5 : 6 respectively. If their salaries were increased by 50 per cent, 60 per cent and 50 per cent respectively, what will be the new ratio of the salaries of Akhil, Arun and Karthik ?
Options- A. 6 : 8 : 9
- B. 8 : 6 : 9
- C. 9 : 8 : 6
- D. 6 : 5 : 4 Also asked in: GRE, GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 9 : 8 : 6
Explanation:
Given the salaries are in the ratio of 4 : 5 : 6
Now the salaries are increased by 50%, 60% and 50% respectively
The New ratio of salaries will be
4 x (150/100) : 5 x (160/100) : 6 x (150/100)
= 6 : 8 : 9
The new ratio of salaries of Akhil, Arun and Karthik is 9 : 8 : 6
- 8. In an exam, a candidate secured 504 marks out of the maximum mark of 'M'. If the maximum mark 'M' is converted into 800 marks, he would have secured 384 marks. What is the value of 'M' ?
Options- A. 910
- B. 1000
- C. 970
- D. None of the above Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: None of the above
Explanation:
504/M = 384/800
(504 x 800) / 384 = M
M = 1050
- 9. A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.
Options- A. 8 Liters
- B. 10 Liters
- C. 18 Liters
- D. 22 Liters Discuss
Correct Answer: 10 Liters
Explanation:
Let the quantity of alcohol and water be 4x liters and 3x liters respectively. Then,
(4x)/(3x+5) = 4/5
=> 20x = 4(3x+5)
=> x = 2.5
Quantity of alcohol = (4 * 2.5) liters = 10 liters.
- 10. A, B and C have amounts in the ratio of 3 : 4 : 5. First B gives 1/4th to A and 1/4th to C then C gives 1/6th to A. Find the final ratio of amount of A, B and C respectively.
Options- A. 4:3:5
- B. 5:4:3
- C. 3:4:5
- D. 5:2:5 Discuss
Correct Answer: 5:2:5
Explanation:
A B C
3x 4x 5x
(3x+x) 2x (5x+x) (B Gives 1/4 to A and 1/4 to C)
=4x 2x 6x
(4x+x) 2x 5x ( C Gives 1/6 to A)
=5x 2x 5x
Therefore, 5 : 2 : 5
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