Ratio and Proportion problems
- 1. The ratio of the first and second class fares between two stations is 4 : 1 and that of the number of passengers travelling by first and second class is 1 : 40. If Rs. 1100 is collected as fare, the amount collected from first class passengers is?
Options- A. Rs. 275
- B. Rs. 315
- C. Rs. 315.50
- D. Rs. 100 Discuss
Correct Answer: Rs. 100
Explanation:
Ratio of amounts collected from 1st and 2nd class = (4 x 1 : 1 x 40) = (1 : 10)
?Amount collection as 1st class fare = Rs. (1100 x 1/11) = Rs.100
- 2. The students in three classes are in the ratio 2 : 3 : 5. If 20 students are increased in each class. The ratio changes to 4 : 5 : 7. The total number of students before the increase were?
Options- A. 10
- B. 90
- C. 100
- D. None of these Discuss
Correct Answer: 100
Explanation:
Let the number of students be 2x, 3x and 5x
? (2x + 20) : (3x + 20) : (5x + 20) = 4 : 5 : 7
? (2x + 20)/4 = (3x + 20)/5 = (5x + 20)/7
? 5(2x + 20) = 4(3x + 20)
? x = 10
Hence, total number of student before increase = 10x = 100.
- 3. One year ago the ratio between Laxman's and Gopal's salary was 3 : 4. The ratio of their individual salaries between last year's and this year's salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs. 4,160. The salary of Laxman now is?
Options- A. Rs. 1040
- B. Rs. 1600
- C. Rs. 2560
- D. Rs. 3120 Discuss
Correct Answer: Rs. 1600
Explanation:
Let the salaries of Laxman and Gopal one year before be x1 ,y1 respectively.
? x1/y1 = 3/4 ......(1)
x2 + y2 = 4160 .....(2)
From equations (1) and (2)
x2 = Rs. 1600.
- 4. Three students A, B and C hired a computer for a month. A runs 27 floppy dics for 19 days, B runs 21 for 17 days and C runs 24 for 23 days. If at the end of the month, the rent amounts to ? 23700, how much amount outght to be paid by A?
Options- A. ? 8550
- B. ? 5950
- C. ? 9200
- D. ? 6750 Discuss
Correct Answer: ? 8550
Explanation:
Floppy - days = Number of floppies X Days run
Here, A's floppy - days : B 's floppy - days : C's floppy - days = A's payment for rent : B 's payment for rent : C's payment for rent
= 27 x 19 : 21 x 17 : 24 x 23
A's rent : B's rent : C's rent = 171 : 119 : 184
? Payment for rent by A = [171/(171 + 119 + 184)] x 23700 = ? 8550
- 5. The work done by (x + 2) men in (x - 3) days and work done by x men in (x - 2) days are equal. Find the value of x.?
Options- A. 6
- B. 4
- C. 8
- D. 9 Discuss
Correct Answer: 6
Explanation:
Work done by (x + 2 ) men in (x - 3) days = (x + 2) (x - 3)
Work done by x men in (x - 2) days = x(x - 2)
? (x + 2) (x - 3) = x(x - 2)
On Solving, we get x = 6
- 6. 1 yr ago, the ratio between mother and daughter age was 4 : 1. The ratio of their ages after 4 yr will be 3 : 1. Find the ratio of their ages 5 yr ago?
Options- A. 6 : 1
- B. 1 : 6
- C. 2 : 3
- D. 3 : 2 Discuss
Correct Answer: 6 : 1
Explanation:
Let the present age of mother be x and daughter be y.
From question,
(x - 1)/(y - 1) = 4/1
? x - 1 = 4(y - 1)
? x = 4y - 3 ......(i)
Again from question,
(x + 4)/(y + 4) = 3/1
? x + 4 = 3(y + 4)
? x = 3y + 8 ..(ii)
On Solving Eqs. (i) and (ii), we get y = 11 and x = 41
? Ratio of their ages 5 yr ago = (x - 5)/(y - 5) = 36/6 = 6/1 = 6 : 1
- 7. The ratio of expenditure and saving of a person is 26 : 3 . If his monthly income is ? 7250, then what is his monthly savings?
Options- A. ? 290
- B. ? 350
- C. ? 750
- D. ? 780 Discuss
Correct Answer: ? 750
Explanation:
Let the expenditure and saving be ? 26y and ? 3y, respectively.
Then, according to the question,
26y + 3y = 7250
? 29y = 7250
? y = 7250/29
? y = 250
So, his monthly saving is (250 x 3) i., e ? 750
- 8. Three hikers A, B and C start on a trip with ? 50 each and agree to share the expenses equally. If at the end of the trip, A has ? 20 left with him, B ? 30 and ? 40, by how much amount must they settle their accounts?
Options- A. A must pay ? 10 to C
- B. C must pay ? 10 to B
- C. B must pay ? 10 to C
- D. C must pay ? 10 to A Discuss
Correct Answer: C must pay ? 10 to A
Explanation:
They start with total of (50 x 3) = ? 150 and they return after the trip with (20 + 30 + 40) = ? 90.
So, to settle their accounts, each person must have 90/3 = ? 30 with them,
Hence, C must pay ? 10 to A
- 9. ? 1290 is divided between A, B and C, so that A's share is 1 1/ 2 times B's share and B's share is 1 3/ 4 C's share. What is C's share?
Options- A. ? 200
- B. ? 400
- C. ? 240
- D. ? 420 Discuss
Correct Answer: ? 240
Explanation:
A : B = 11/2 = 3 : 2 = 3 x 7 : 2 x 7 = 21 : 14
B : C = 13/4 : 1 = 7 : 4 = 7 x 2 : 4 x 2 = 14 : 8
? A : B : C = 21 : 14 : 8
? C's share = [8/(21 + 14 + 8)] x 1290 = ? 240
- 10. A started a business with a capital of ? 10000 and 4 months later , B joined him with a capital of ? 5000. What is the share of A in the total profit of ? 2000 at the end of the year?
Options- A. ? 800
- B. ? 1000
- C. ? 1500
- D. ? 1800 Discuss
Correct Answer: ? 1500
Explanation:
Profit of A/Profit of B = (Amount x Number of months) / (Amount x Number of months)
= (10000 x 12)/(5000 x 8) = 3/1
? Profit share of A = [3/(3 + 1)] x 2000 = ? 1500
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