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- Question
- From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is 4 times as large as the smaller number. What is the ratio of the numbers?
Options- A. 5 : 2
- B. 1 : 4
- C. 4 : 1
- D. 4 : 5
- Correct Answer
- 5 : 2
ExplanationLet the smaller number = M and the greater number = N
According to the question ,
(N - M/2) = 4(M - M/2)
? N - M/2 = 4M/2
? N = 2M + M/2
? N = 5M/2
? N : M = 5 : 2 - 1. The ratio between two number is 3 : 4. if each number is increased by 3, the ratio becomes 4 : 5. Find the differences between the numbers.
Options- A. 3
- B. 9
- C. 2
- D. 7 Discuss
- 2. One - half of a certain number is equal to 65% of the 2nd number. Find the ratio of 1st to 2nd number.
Options- A. 10 : 13
- B. 8 : 13
- C. 13 : 8
- D. 13 : 10 Discuss
- 3. If a + b : b + c : c + a = 6 : 7 : 8 and a + b + c = 14, then find c?
Options- A. 6
- B. 7
- C. 8
- D. 10 Discuss
- 4. In a certain school, the ratio of boys to girls is 7 : 5. If there are 2400 students in the school, then how many girls are there in the school?
Options- A. 500
- B. 700
- C. 800
- D. 1000 Discuss
- 5. In a mixture of 60 L, the ratio of milk and water is 2 : 1. If the ratio of milk and water is to be 1 : 2, then the amount of water to be further added must be?
Options- A. 40 L
- B. 30 L
- C. 20 L
- D. 60 L Discuss
- 6. Two number are in the ratio of 2 : 3. If 9 is added to each number, they will be in the ratio 3 : 4. What is the product of the two numbers?
Options- A. 360
- B. 480
- C. 486
- D. 512 Discuss
- 7. Weekly income of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves ? 300 per week, then the weekly income of the first person is?
Options- A. ? 7500
- B. ? 4500
- C. ? 6300
- D. ? 5400 Discuss
- 8. Amit and Sudesh have invested in the ratio of 4 : 7. If both invested a total amount of ? 49500, then find the investment of Sudesh?
Options- A. ? 31500
- B. ? 1800
- C. ? 31000
- D. ? 18500 Discuss
- 9. A bag contains ? 1, 50 paise and 25 paise coins in the ratio of 8 : 9 : 11. If the total money in the bag is ? 366, then find the number of 25 paise coins?
Options- A. 264
- B. 364
- C. 241
- D. 245 Discuss
- 10. If sum of ? 1664 is divided between P and Q in the ratio of 1/3 : 1/5, then find P's share?
Options- A. 1085
- B. 1015
- C. 1090
- D. 1040 Discuss
Ratio and Proportion problems
Search Results
Correct Answer: 3
Explanation:
Let the number be 3k and 4k.
According to the question,
(3k + 3)/(4k+ 3) = 4/5
? 5(3k + 3 ) = 4(4k + 3)
? 15k + 15 = 16k + 12
? k = 15 - 12 = 3
? Difference between the numbers = (4k - 3k) = k = 3
Correct Answer: 13 : 10
Explanation:
Let 1st number = x and 2nd number = y
According to the question 1/2 of x = 65% of y
? x/y = 130/100 = 13/10
? x : y = 13 : 10
Correct Answer: 10
Explanation:
Let a + b = 6k, b + c = 7k, c + a = 8k ...(i)
and a + b + c = 14 ...(ii)
From Eq. (i),
a + b + b + c + c + a = 6K + 7K + 8K
? 2(a + b + c) = 21K
? 2 x 14 = 21K
? K = 28/21 = 4/3
? a + b 6k = = 6 x 4/32 = 8
Subtracting Eq. (iii) from Eq. (ii), we get
(a + b + c) - (a + b) = 14 - 8 = 6
Correct Answer: 1000
Explanation:
Let the number of boys and girls are 7k and 5k, respectively.
Given, total number of students = 2400
? 7k + 5k = 2400
? 12k = 2400
? k = 200
? Required number of girls = 5k = 5 x 200 = 1000
Correct Answer: 60 L
Explanation:
Milk = (2/3) x 60 = 40 L
Water = (1/3) x 60 = 20 L
Water added = W L
Now, 40/(20 + W) = 1/2
? W = 60 L
Correct Answer: 486
Explanation:
Let the number be M and N
According to the question.
M/N = 2/3
? 3M = 2N
? 3M - 2N = 0 ...(i)
And (M + 9)/(N + 9) = 3/4
? 4M + 36 = 3N + 27
? 4M - 3N = -9 ...(ii)
Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27
Now, putting N = 27 in Eq. (i), we get 3M = 54
? M = 18
? Product of the given numbers = 27 x 18 = 486
Correct Answer: ? 6300
Explanation:
Let the income of two persons are 7k and 3k
Expenditure of first person = 7k - 300
Expenditure of second person = 3k - 300
According to the question,
(7k - 300)/(3k - 300) = 5/2
? 14k - 600 = 15k - 1500
? k = 900
Income of first person = 7k = 7 x 900
= ? 6300
Correct Answer: ? 31500
Explanation:
Given total amount = ? 49500
Let part of Amit's investment = 4k
and part of sudesh's investment = 7k
According to the question
4k + 7k = 49500
? 11k = 49500
? k = 49500/11
? k = 4500
Hence investment of sudesh = 7k = 7 x 4500 = 31500
Correct Answer: 264
Explanation:
Let number of ? 1 coins = 8k
Number of 50 paise coins = 9k
Number of 25 paise coins = 11k
According to the question,
8k + 9k/2 + 11k/4 = 366
? 32k + 18k + 11k = 1464
? 61k = 1464
? k = 1464/61 = 24
? Number of 25 paise coins = 11k = 11 x 24 = 264
Correct Answer: 1040
Explanation:
Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3
Here, a = 5, b = 3, N = 1664
P's share = a/(a + b) x N
? = 5/(5 + 3) x 1664 = (5/8) x 1664 = ? 1040
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