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How-much-money-will-A-gets-when-Rs-2430-is-divided-among-A-B-and-C-such-that-if-their-shares-be-diminished-by-Rs-5-Rs-10-Rs-15-respectively-the-remainders-shall-be-in-the-ratio-3-4-5




Question Number 9212 by nazar last updated on 23/Nov/16
How much money will A gets when    Rs. 2430 is  divided  among   A, B and C such that if their shares be  diminished by Rs. 5, Rs. 10, Rs. 15   respectively, the remainders shall be  in the ratio 3 : 4 : 5.
$$\mathrm{How}\:\mathrm{much}\:\mathrm{money}\:\mathrm{will}\:\mathrm{A}\:\mathrm{gets}\:\mathrm{when}\: \\ $$$$\:\mathrm{Rs}.\:\mathrm{2430}\:\mathrm{is}\:\:\mathrm{divided}\:\:\mathrm{among}\: \\ $$$$\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{such}\:\mathrm{that}\:\mathrm{if}\:\mathrm{their}\:\mathrm{shares}\:\mathrm{be} \\ $$$$\mathrm{diminished}\:\mathrm{by}\:\mathrm{Rs}.\:\mathrm{5},\:\mathrm{Rs}.\:\mathrm{10},\:\mathrm{Rs}.\:\mathrm{15}\: \\ $$$$\mathrm{respectively},\:\mathrm{the}\:\mathrm{remainders}\:\mathrm{shall}\:\mathrm{be} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{3}\::\:\mathrm{4}\::\:\mathrm{5}. \\ $$
Answered by mrW last updated on 23/Nov/16
Sum of remainders: 2430−(5+10+15)=2400  A=(3/(3+4+5))×2400+5=(3/(12))×2400+5=Rs. 605  B=(4/(3+4+5))×2400+10=(4/(12))×2400+10=Rs. 810  C=(5/(3+4+5))×2400+15=(5/(12))×2400+15=Rs. 1015
$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{remainders}:\:\mathrm{2430}−\left(\mathrm{5}+\mathrm{10}+\mathrm{15}\right)=\mathrm{2400} \\ $$$$\mathrm{A}=\frac{\mathrm{3}}{\mathrm{3}+\mathrm{4}+\mathrm{5}}×\mathrm{2400}+\mathrm{5}=\frac{\mathrm{3}}{\mathrm{12}}×\mathrm{2400}+\mathrm{5}=\mathrm{Rs}.\:\mathrm{605} \\ $$$$\mathrm{B}=\frac{\mathrm{4}}{\mathrm{3}+\mathrm{4}+\mathrm{5}}×\mathrm{2400}+\mathrm{10}=\frac{\mathrm{4}}{\mathrm{12}}×\mathrm{2400}+\mathrm{10}=\mathrm{Rs}.\:\mathrm{810} \\ $$$$\mathrm{C}=\frac{\mathrm{5}}{\mathrm{3}+\mathrm{4}+\mathrm{5}}×\mathrm{2400}+\mathrm{15}=\frac{\mathrm{5}}{\mathrm{12}}×\mathrm{2400}+\mathrm{15}=\mathrm{Rs}.\:\mathrm{1015} \\ $$

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