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Let the money invested by C be Rs.x.

Therefore, According to the question;

Investment of B= Rs.90/100 * x (given)

Investment of C= Rs.x (assumed)

Investment of A= Rs.110/100 * B (given)

But, B= Rs.90/100 * x

therefore,

A= Rs.110/100*90/100*x

But, A+B+C= Rs.5780

or, 110/100*90/100*x + 90/100*x + x = 5780

or, 99/100x +90/100x +100/100x = 5780 (solving and taking L.C.M=100)

or, 289/100x = 5780 or, x = 5780*100/289 or, x = Rs. 2000/-