Simple Interest Quiz Set 010

We know, I = PRT/100. If I = P/4, then $1/4$ = RT/100. So R = $100/{4 × 5}$ = 5%.

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 13 × 17 × 4 = 884. Thus, the three parts are in the ratio $68 : 52 : 221$. The parts are: 57970 × $221/{68 + 52 + 221}$, 57970 × $52/{68 + 52 + 221}$ and 57970 × $68/{68 + 52 + 221}$, which are 11560, 8840 and 37570. The smaller is Rs. 8840.

We should use the shortcut technique here. If r₁, t₁, r₂, t₂ be the rates and times for two parts with same interest amount, then the two parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2}$. In our case r₁ = r₂ = 10, which cancels, so the ratio is $1/t_1 : 1/t_2$. Thus, the two parts are in the ratio $t_2 : t_1$. The parts are: 3420 × $7/{12 + 7}$, and 3420 × $12/{12 + 7}$, which are 1260 and 2160. The smaller is Rs. 1260.

Let the amount x be invested at r1% and remaining (P - x) at r2%, and let the sum of interests be I. Then, I = ${x × r_1 × 5}/100$ + ${(P - x) × r_2 × 5}/100$, which simplifies to 100I = 5 × ($x × (r_1 - r_2) + P × r_2$). Putting r₁ = 12, r₂ = 6, P = 1100, I = 510, we get x = Rs. 600.

Shortcut is required here. The addition would be same as if R = 2%, T = 7 years and P = Rs. 4200, which is ${4200 × 2 × 7}/100$ = 588. So new amount is 6258 + 588 = Rs. 6846.