A sum of Rs. 7930 is divided into 3 parts and given at loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of = ?

Explanation:-

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = {\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = {\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right) \cr & \,\,\,\,\,{\text{110A}}\,\,\,\,\,{\text{ = }}\,\,\,\,\,{\text{115B}}\,\,\,\,\,{\text{ = }}\,\,\,\,\,{\text{120C}} \cr & \,\,\,\,\,{\text{22A}}\,\,\,\,\,{\text{ = }}\,\,\,\,\,{\text{23B}}\,\,\,\,\,{\text{ = }}\,\,\,\,\,{\text{24C}} \cr}$$
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{ & {\text{276 : 264 : 253}} \cr & {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr}$$