Question 1:
Divide Rs.2379 into 3 parts so that their amounts after 2,3 and 4 years respectively may be equal ,the rate of interest being 5% p.a. at simple interest .The first part is:
A. 792
B. 759
C. 828
Feedback Let the parts be x , y ,z
R = 5 %
Corresponding Interest = [ x + interest on x for 2 years = y + interest on y for 3 years = z + interest on z for 4 years]
=> ( x + ( x * 5 * 2 / 100) = ( y + ( y * 5 * 3 / 100 ) = ( z + ( z * 5 * 4 / 100)
=>( x + (x / 10)) = ( y + ( 3y / 20)) = ( z + ( z / 5))
=> (11x / 10) = (23y / 20) = (6z / 5)
Let (11x / 10) = (23y / 20) = (6z / 5) = k ( where k is a constant)
Then x =10 k /11,y=20 k / 23,z=5 k / 6
We know that x + y + z = 2379
=> 10 k / 11+ 20 k / 23 + 5k / 6=2379
=> 10 k * 23 * 6 + 20 k + 11 * 6 + 5 k * 23 *11 => 2379 * 11 * 23 *6
=> 1380 k + 1320 k + 1265 k = 2379 * 11 * 23 *6
=>3965 k = 2379 * 11 * 23 *6
=> k = 2379 * 11 * 23 *6 / 3965
First part, x = 10k / 11
Substituting k = 2379 * 11 * 23 *6 / 3965, we get
=> 10 / 11 * 2379 * 11 * 23 *6 / 3965
= 2 * 3 * 23 * 6
= 6 * 23 * 6
= 23 * 36
= 828
First part Rs = 828
D. 818

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