A sum becomes 500 in 5 years and 600 in 7 years at a certain rate percent p. a. at of simple interest. what is the sum?

Sum is 250 , Rate is 20% per annum

P=_5yr__500___2yr__600

i.e in 2yrs si is 100,i.e in 1 yr 50rs,lly in 5yrs it will be 250rs

p=250rs
si=250 in 5 yrs
1yr si =50re
rate =50/250=20%

5yr=500
7yr=600

diff of yr =2
diff in amount=100
per year SI =50

so in 5yrs =5×50=250
so PA =250

and the rate is 50/250=1/5=20percent
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easy
just form an euqation for the both amounts and calculate interest

Also explain it