May 17th, 2018, 03:19 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  How to solve this crazy problem?
A Certain sum amounts to 41280 in 6 years and to 29760 in 2 years at S.I. Find the sum and the rate of interest? Answer is 24000 and 12% p.a Usually they used to give one P or one T (time). But here they gave two different amounts and two different times and asking me to find one sum and one rate of interest. I am totally confused. Please help me. 
May 17th, 2018, 04:15 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,551 Thanks: 2554 Math Focus: Mainly analysis and algebra 
You can form two equations each having the amount and the interest rate as variables. Using those equations, you can eliminate one variable and thus solve for the other. Substitute and solve for the remaining variable.

May 17th, 2018, 05:47 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,785 Thanks: 970 
a = start sum, r = rate Code: YEAR BALANCE 0 a 2 29760 = a + 2*a*r [Eq 1] 6 41280 = a + 6*a*r [Eq 2] 
May 17th, 2018, 10:34 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1 
Now should I have to eliminate R and find P?

May 17th, 2018, 10:42 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,785 Thanks: 970 
Yes, and EASY to do: 2 equations and 2 variables. Get to work! 
May 17th, 2018, 10:51 AM  #6  
Senior Member Joined: May 2008 Posts: 298 Thanks: 81  Beer soaked ramblings follow. Quote:
Ah Sir D, didst thou also forgot Ganesh' command for you to give a complete worked out solution instead of half baked cryptic clues that will force Ganesh to actually do some real work?  
May 17th, 2018, 10:01 PM  #7 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1 
I got the answer.

May 18th, 2018, 05:12 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,785 Thanks: 970 
Congratulations! Why don't you show your steps to solving, as it may help a student: this is main purpose of this site... 
May 18th, 2018, 05:33 AM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,551 Thanks: 2554 Math Focus: Mainly analysis and algebra  
May 18th, 2018, 06:37 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,095 Thanks: 1905 
By subtraction, 11520 = 4ar, so 5760 = 2ar. Hence a = 29760  5760 = 24000, and so r = 5760/48000 = 0.12 = 12%. There are various other ways of solving the two equations. 

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