A sum of Rs. 2,310 is divided between A, B and C such that the ratio of the shares of B and C is 3:5 and the ratio of the shares of C and A is 4:9. What is the difference (in Rs.) between the shares of A and C?
- A990
- B750
- C450
- D240
Solution & Step-by-step Explanation
Given ratios:
B:C=3:5
C:A=4:9
To combine the ratios, make the value of C equal in both ratios (LCM of 5 and 4 is 20):
B:C=3×4:5×4=12:20
C:A=4×5:9×5=20:45
Thus, the combined ratio is:
A:B:C=45:12:20
Total parts = 45+12+20=77 units.
Given total sum = Rs. 2,310:
77 units=2310⟹1 unit=
77
2310
=30
The difference between the shares of A and C is:
Difference=A−C=45−20=25 units
Difference=25×30=Rs. 750
B:C=3:5
C:A=4:9
To combine the ratios, make the value of C equal in both ratios (LCM of 5 and 4 is 20):
B:C=3×4:5×4=12:20
C:A=4×5:9×5=20:45
Thus, the combined ratio is:
A:B:C=45:12:20
Total parts = 45+12+20=77 units.
Given total sum = Rs. 2,310:
77 units=2310⟹1 unit=
77
2310
=30
The difference between the shares of A and C is:
Difference=A−C=45−20=25 units
Difference=25×30=Rs. 750