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Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 and 15 diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9. what is the share of B?
- a)360
- b)362
- c)365
- d)370
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 an...
Sum of money to be divided = 1087
Total money withdrawn from A, B and C = (10 + 12 + 15) = 37
Now remainders = 1087 - 37 = 1050 which will be divided in the proportion 5, 7, 9.
Share of B out of 1050 = 7/21 × 1050 = 7 × 50 = 350
Total share of B = 350 + 12 = 362
Most Upvoted Answer
Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 an...
Let the shares of A, B, and C be x, y, and z respectively.
Given:
x + y + z = 1087 ----(1) (Sum of their shares is 1087)
If Rs. 10, 12, and 15 are diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9.
According to the given information:
(x - 10) / (y - 12) = 5/7 ----(2)
(x - 10) / (z - 15) = 5/9 ----(3)
Solving equations (2) and (3), we can find the values of x, y, and z.
To solve these equations, let's equate the numerator in both equations:
(x - 10) / (y - 12) = (x - 10) / (z - 15)
Cross multiplying, we get:
(x - 10)(z - 15) = (x - 10)(y - 12)
Expanding and simplifying, we get:
xz - 15x - 10z + 150 = xy - 12x - 10y + 120
Rearranging the terms, we get:
xz - xy - 15x + 12x - 10z + 10y = 120 - 150
Simplifying further, we get:
x(z - y - 3) + 2y - 10z = -30 ----(4)
Similarly, let's equate the denominators in equations (2) and (3):
(y - 12)(z - 15) = (y - 12)(x - 10)
Expanding and simplifying, we get:
yz - 15y - 12z + 180 = xy - 10x - 120
Rearranging the terms, we get:
xy - yz - 12z + 10x + 15y = 180 + 120
Simplifying further, we get:
x(y - z + 10) + 15y - 12z = 300 ----(5)
Now, we have equations (4) and (5) with two equations and two variables. We can solve these equations to find the values of x, y, and z.
To solve these equations, let's multiply equation (4) by 15 and equation (5) by 2:
15x(z - y - 3) + 30y - 150z = -450 ----(6)
2x(y - z + 10) + 30y - 24z = 600 ----(7)
Adding equations (6) and (7), we get:
15x(z - y - 3) + 2x(y - z + 10) + 30y - 150z + 30y - 24z = -450 + 600
Simplifying, we get:
15xz - 15xy - 45x + 2xy - 2xz + 20x + 60y - 174z = 150
Combining like terms, we get:
-45x + 20x + 60y - 174z = 150
Simplifying further
Given:
x + y + z = 1087 ----(1) (Sum of their shares is 1087)
If Rs. 10, 12, and 15 are diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9.
According to the given information:
(x - 10) / (y - 12) = 5/7 ----(2)
(x - 10) / (z - 15) = 5/9 ----(3)
Solving equations (2) and (3), we can find the values of x, y, and z.
To solve these equations, let's equate the numerator in both equations:
(x - 10) / (y - 12) = (x - 10) / (z - 15)
Cross multiplying, we get:
(x - 10)(z - 15) = (x - 10)(y - 12)
Expanding and simplifying, we get:
xz - 15x - 10z + 150 = xy - 12x - 10y + 120
Rearranging the terms, we get:
xz - xy - 15x + 12x - 10z + 10y = 120 - 150
Simplifying further, we get:
x(z - y - 3) + 2y - 10z = -30 ----(4)
Similarly, let's equate the denominators in equations (2) and (3):
(y - 12)(z - 15) = (y - 12)(x - 10)
Expanding and simplifying, we get:
yz - 15y - 12z + 180 = xy - 10x - 120
Rearranging the terms, we get:
xy - yz - 12z + 10x + 15y = 180 + 120
Simplifying further, we get:
x(y - z + 10) + 15y - 12z = 300 ----(5)
Now, we have equations (4) and (5) with two equations and two variables. We can solve these equations to find the values of x, y, and z.
To solve these equations, let's multiply equation (4) by 15 and equation (5) by 2:
15x(z - y - 3) + 30y - 150z = -450 ----(6)
2x(y - z + 10) + 30y - 24z = 600 ----(7)
Adding equations (6) and (7), we get:
15x(z - y - 3) + 2x(y - z + 10) + 30y - 150z + 30y - 24z = -450 + 600
Simplifying, we get:
15xz - 15xy - 45x + 2xy - 2xz + 20x + 60y - 174z = 150
Combining like terms, we get:
-45x + 20x + 60y - 174z = 150
Simplifying further
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Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 and 15 diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9. what is the share of B?a)360b)362c)365d)370Correct answer is option 'B'. Can you explain this answer?
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Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 and 15 diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9. what is the share of B?a)360b)362c)365d)370Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 and 15 diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9. what is the share of B?a)360b)362c)365d)370Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rs. 1087 among A, B, C are divided in such a way that if Rs. 10, 12 and 15 diminished from their shares respectively, the remainders will be in the ratio of 5, 7, 9. what is the share of B?a)360b)362c)365d)370Correct answer is option 'B'. Can you explain this answer?.
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