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Rs. 3000 are divided amongst A, B and C, so that if Rs. 20, Rs. 40 and Rs. 60 be taken from their shares respectively, they will have money in the ratio 3 ∶ 4 ∶ 5. Find the shares of C.
- a)1260
- b)1360
- c)1270
- d)1370
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Rs. 3000 are divided amongst A, B and C, so that if Rs. 20, Rs. 40 and...
Total decrease = 3000 - 120 = 2880
C’s share = 5/12 × 2880 = 5 × 240 = 1200
Share of C out of 3000 = 1200 + 60 = 1260
Most Upvoted Answer
Rs. 3000 are divided amongst A, B and C, so that if Rs. 20, Rs. 40 and...
Solution:
Let the shares of A, B, and C be x, y, and z respectively.
Given:
- Total sum of money = Rs. 3000
- After deducting Rs. 20, Rs. 40, and Rs. 60 from their shares, the ratio becomes 3:4:5
Equations:
- x + y + z = 3000
- (x - 20) : (y - 40) : (z - 60) = 3 : 4 : 5
Equation 1:
x + y + z = 3000
Equation 2:
(x - 20) / 3 = (y - 40) / 4 = (z - 60) / 5
Solving Equations 1 and 2:
- From Equation 2, we get:
x - 20 = 3a
y - 40 = 4a
z - 60 = 5a
- Adding all three equations, we get:
x + y + z - 120 = 12a
3000 - 120 = 12a
2880 = 12a
a = 240
- Substituting the value of a back in the equations:
x - 20 = 3 * 240
x = 720
y - 40 = 4 * 240
y = 960
z - 60 = 5 * 240
z = 1200
Hence, the share of C (z) is Rs. 1200.
Therefore, the correct option is 1260.
Let the shares of A, B, and C be x, y, and z respectively.
Given:
- Total sum of money = Rs. 3000
- After deducting Rs. 20, Rs. 40, and Rs. 60 from their shares, the ratio becomes 3:4:5
Equations:
- x + y + z = 3000
- (x - 20) : (y - 40) : (z - 60) = 3 : 4 : 5
Equation 1:
x + y + z = 3000
Equation 2:
(x - 20) / 3 = (y - 40) / 4 = (z - 60) / 5
Solving Equations 1 and 2:
- From Equation 2, we get:
x - 20 = 3a
y - 40 = 4a
z - 60 = 5a
- Adding all three equations, we get:
x + y + z - 120 = 12a
3000 - 120 = 12a
2880 = 12a
a = 240
- Substituting the value of a back in the equations:
x - 20 = 3 * 240
x = 720
y - 40 = 4 * 240
y = 960
z - 60 = 5 * 240
z = 1200
Hence, the share of C (z) is Rs. 1200.
Therefore, the correct option is 1260.
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