# On what date will Rs.1,950 lent on 5th January, 2011 amount to Rs. 2,125.50 at 5 per cent per annum simple interest ? if the interest on Rs. 2,400 be more than the interest on Rs. 2,000 by Rs.60 in 3 years at the same rate per cent; find the rate.

1
by raniabsmarkoserani

2015-06-03T19:59:22+05:30
1.SI=A-P=Rs.2125.50-Rs.1950
=Rs.175.50
R=5%
T=100*SI/(R*P)=100*175.50/(5*1950)
or, T=1.8 years.
=1 year +0.8 years.
=1 year + 8/10*365 days
=1 year and 292 days.
The required date will be 1 year and 292 days later 5th Jan 2011.
The next year is 2012 .
Note that the number of days (in total) is 365+292=657 but here we will take 658 days into account since a leap year has 1 extra day.
The required date=(30-5)+31+31+30+31+30+31+31+29+31+30+31+30+31+31+30+31+30+31+31+28+(31-7) By trial and error method is 24th March 2013.
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2.Let the rate be x%.
1st case:
P=Rs.2400 ,T=3 y , R=x%
⇒SI=P*R*T⇒2400*3*x/100=72x.
2nd case:
P=Rs.2000 ,T=3y , R=x%
⇒SI=P*R*T⇒2000*3*x/100=60x.
Given , 72x-60x=60.
⇒12x=60
⇒x=60/12=5.
Ans:The rate is 5% p.a.
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