Simple Interest Quiz Set 004

Let the amount x be invested at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 3}/100$ + ${(P - x) × r_2 × 3}/100$, which simplifies to 100I = 3 × ($x × (r_1 - r_2) + P × r_2$). Putting r₁ = 11, r₂ = 6, x = 800, I = 246, we get P = Rs. 700.

Let the amounts be x and y. We have x × r₁ × t₁ = y × r₂ × t₂. We can see that x : y is same as r₂t₂ : r₁t₁. The ratio is (5 × 3) : (3 × 5) = 15 : 15, or same as 1. Please note that the answer is independent of the value of the total amount.

We should use the shortcut technique here. If r₁, t₁, r₂, t₂ and r₃, t₃ be the rates and times for three parts with same interest amount, then the three parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2} : 1/{r_3 t_3}$. In our case r₁ = r₂ = r₃ = 10, which cancels, so the ratio is $1/t_1 : 1/t_2 : 1/t_3$. The product of denominators is 4 × 7 × 17 = 476. Thus, the three parts are in the ratio $119 : 68 : 28$. The parts are: 23650 × $28/{119 + 68 + 28}$, 23650 × $68/{119 + 68 + 28}$ and 23650 × $119/{119 + 68 + 28}$, which are 13090, 7480 and 3080. The smaller is Rs. 3080.

If I is the interest, and principal is P, time is P, and rate is P, then, I = $(P × P × P)/100$. Which gives P = $√^3{100 × I}$, which is $√^3{100 × 5120}$, which is $√^3{1000 × 8 × 8 × 8}$ = Rs. 80.

I = P × (1/4), so we can write P × (1/4) = P × (R/100) × R. Cancelling P and solving for R, we get, R = $√{100 × 1/4}$ = 5%.