Question

Divide Rs. 7154 among A B C D so that share of A:B is 2:5 and that of b and c are in the ratio 4:7 and that of c and d are in the ratio 9:13

Answer 1

this is your answer little soul ...

Answer 2

given a sum amount to be divided between A, B, C and D in given rations, find the amount received by each one.

Explanation:

1. let the amount's share received by A, B, C, and D be denoted by a, b, c, and d respectively and total amount be denoted by 'T'. then we have,                       $T=a+b+c+d=7154$    ----(a)
2. given that ratio of shares of A and B are $2:5$. then we have,                                    $\frac{a}{b} =\frac{2}{5}\ \ \ \ \ \ \ =>b=\frac{5}{2}a$     ----(b)
3. given that ratio of shares of B and C are $4:7$ then we have,                                   $\frac{b}{c} =\frac{4}{7}\ \ \ \ \ \ \ =>c=\frac{7}{4}b$                                                                                               from (b) we get,    $c=\frac{35}{8} a$     ----(c)
4. given that ration of shares of C and D are $9:13$ then we have,                                               $\frac{c}{d} = \frac{9}{13} \ \ \ \ \ \ => d=\frac{13}{9}c$                                                                                                            from (c) we get,  $d=\frac{455}{72} a$ ----(d)
5. putting values from (b), (c), (d) in (a) we get,                                                         $a(1+\frac{5}{2} +\frac{35}{8} +\frac{455}{72} )=7154 \\a\frac{1022}{72}=7154 \\a=504$  
6. hence from (b), (c), and (d) we get,                                                                       $a=Rs.\ 504\\\\b=\frac{5}{2}(504)\ \ \ \ \ \ \ =>b= Rs.\ 1260\\\\c=\frac{35}{8}(504)\ \ \ \ \ \ =>c=Rs.\ 2205 \\\\b=\frac{455}{72}(504)\ \ \ \ \ =>d= Rs.\ 3185$            --------->ANSWER