10.
Divide Rs 16875 into two parts such that the interest at 7/2 % p.a. for 2 years on one part is equal to the other at 4 % p.a. for 5 years.


A:

Let the Principal of one part = `X` Rs
The Principal of second part = `( 16875  X )` Rs
For one part, `P = X` Rs, `R = 7/2 %, N = 2` years
`SI = (P*R*N)/100`
`SI = ( X * 7/2 * 2 ) / 100 = (7 * X)/100 >(1)`
Now for second part, `P = ( 16875  X ) Rs, R = 4 %, N = 5` years
`SI = (P*R*N)/100`
`SI = (( 16875  X ) * 4 * 5 ) / 100 = (20 * ( 16875  X ))/100 >(2)`
Interest is the same as `(1) = (2)`
`=> (7 * X)/100 = (20 * ( 16875  X ))/100`
`=> 7 X = 20 * ( 16875  X )`
`=> 7 X = 20 * 16875  20 X`
`=> 27 X = 20 * 16875`
`=> X = (20 * 16875) / 27`
`=> X = 12500`
`:.`One part of Principal = Rs `12500` and the second part = Rs `( 16875  12500 )` = Rs `4375`
The two parts are Rs `12500` and Rs `4375` .


