Rajnish invested certain sum in three different schemes P, Q and R with the rates of interest 10% per annum, 12% per annum and 15% per annum, respectively. If the total interest accrued in 1 yr was ? 3200 and the amount invested in scheme R was 150% of the amount invested in scheme Q. what was the amount invested in scheme Q?

Let a, b and c be the amount invested in schemes P, Q and R, respectively.

Then, according to the question,
[(a x 10 x 1)/100] + [(b x 12 x 1)/100] + [(c x 15 x 1)/100] = 3200

? 10a + 12b + 15x = 320000 .....(i)
Now, c = 240% of b = 12b/5 ....(ii)
and c = 150% of a = 3a/2
? a = 2c/3 = (2/3 x 12/5) b = 8b/5 .....(iii)

From Eqs. (i), (ii) and (iii), we get
16b + 12b + 36b = 320000
? 64b = 320000
? b = 5000
? Sum invested in scheme Q = ? 5000