Ratio and Proportion problems
- 1. A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
Options- A. 360, 160, 200
- B. 160, 360, 200
- C. 200, 360,160
- D. 200,160,300 Discuss
Correct Answer: 200, 360,160
Explanation:
let ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
- 2. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Options- A. 2:5
- B. 3:5
- C. 4:5
- D. 5:4 Discuss
Correct Answer: 4:5
Explanation:
Let the third number be x.
Then, first number = 120% of x =120x/100 = 6x/5
Second number =150% of x = 150x/100 = 3x/2
Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5
- 3. 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. 10
- B. 12
- C. 15
- D. 18 Discuss
Correct Answer: 10
Explanation:
Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5) = 4/5
20x = 4(3x+5)
8x = 20
x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
- 4. If Rs. 782 be divided into three parts, proportional to 12:23:34 , then the first part is?
Options- A. Rs. 182
- B. Rs. 190
- C. Rs. 192
- D. Rs. 204 Discuss
Correct Answer: Rs. 204
Explanation:
Given ratio = = 6:8:9
1st part = = Rs. 204
- 5. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?
Options- A. 38000
- B. 46800
- C. 36700
- D. 50000 Discuss
Correct Answer: 38000
Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,
(2x+4000) / (3x+4000) = 40 / 57
? 57 × (2x + 4000) = 40 × (3x+4000)
? 6x = 68,000
? 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
- 6. A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is
Options- A. 35
- B. 40
- C. 45
- D. 50 Discuss
Correct Answer: 40
- 7. The compounded ratio of (2 : 3), (6: 11) and (11 :2) is
Options- A. 1:2
- B. 2:1
- C. 11:24
- D. 36:121 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 2:1
Explanation:
Compounded Ratio :: When we compound two or more ratio's with each other through product or multiplication, the result is simply a compound ratio.
Thus, the product of two or more ratios; i.e, ab:cd is a ratio compounded of the simple ratios a:c and b:d.
Required compounded ratio = (2/3 x 6/11 x 11/2) = 2/1.
- 8. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
Options- A. 10 : 5
- B. 15 : 2
- C. 20 : 2
- D. 25 : 2 Also asked in: GRE
Correct Answer: 25 : 2
Explanation:
Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2
- 9. If 0.75: x :: 5:8, then x is equal to:
Options- A. 1.12
- B. 1.16
- C. 1.20
- D. 1.30 Discuss
Correct Answer: 1.20
Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
- 10. A sum of Rs. 427 is to be divided among A, B and C such that 3 times A?s share, 4 tunes B?s share and 7 times C?s share are all equal. The share of C is :
Options- A. 84
- B. 140
- C. 196
- D. 240 Discuss
Correct Answer: 84
Explanation:
3A = 4B = 7C = k,Then A = k/3, B = k/4 and C= k/7.
A : B : C = k/3 : k/4 : k/7 = 28:21 :12.
Cs share = Rs. [427 x (12/61)] = Rs. 84
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