The sum of present ages of mother and a daughter is 60 years. after 10 years, the product of their ages will be 1500. find their present qges.

Let M and D be the current ages of mother and daughter.

M+D=60 and (M+10)(D+10)=1500.

MD+10(M+D)+100=1500, MD+600+100=1500, so MD=800.

Also, M(60-M)=800, 60M-M^2=800, M^2-60M+800=0=(M-40)(M-20) therefore M=40 (older than daughter) and D=20.

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