Two persons P and Q lent certain amounts at the rate of interest for 2 years and 3 years, respectively, under compound interest. If their final amounts are in the ratio of 3:5, Q's amount at the end of the first year being Rs 8500 and P earned an interest of Rs 510 for the first year, then find the ratio of their principals.

Two persons P and Q lent certain amounts at the rate of interest for 2

1.	Two persons P and Q lent certain amounts at the rate of interest for 2 years and 3 years, respectively, under compound interest. If their final amounts are in the ratio of 3:5, Q's amount at the end of the first year being Rs 8500 and P earned an interest of Rs 510 for the first year, then find the ratio of their principals.
Answer» `33:50` `27:47` `35:61` `22:51` SOLUTION :`P_(1),P_(2)` are the PRINCIPALS of P and Q `(P_(1)(1+R/100)^(2))/(P_(2)(1+R/100)^(3))=3/5` `rArr P_(1)/(P_(2)(1+R/100)) = 3/5 rArr I/8500 = 3/5` `rArr P_(1)=5100`. `(P_(1) xx 1 xx R)/(100)=510` `R=10%` `P_(2)(1+R/100)=8500` `rArr P_(2) = 8500 xx 10/11` `rArr P_(2) = 8500 xx 10/11` `therefore P_(1):P_(2) = 5100,8500 xx 10/11` `=3:50/11=33:50`.