type 4 difference & equality of si rate & years Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Using Rule 1,

Amount lent at 8% rate of interest = Rs.x

Amount lent at $4/3$% rate of interest = Rs.(20,000 - x)

S.I. = ${\text"Principal × Rate × Time"/100$

${x × 8 × 1}/100 + {(20,000 - x) × 4/3 × 1}/100$ = 800

${2x}/25 + {20,000 - x}/75 = 800$

${6x + 20,000 - x}/75 = 800$

5x + 20,000 = 75 × 800 = 60,000

5x = 60,000-20,000 = 40,000

$x = {40,000}/5$ = Rs.8000

Answer: (a)

${P × r × 1}/100 = {P × 5 × 2}/100$

[Since,Capital is same in both cases]

r × 1 = 5 × 2 = 10%

Answer: (a)

We know that

S.I. = $\text"PRT"/100$

According to question,

S.I.= $4/9P$ & R = T (numerically)

$4/9P = {P × R × R}/100$

$R^2 = 400/9$

R = $√{400/9} = 20/3 = 6{2}/3$%

Answer: (d)

Let amount invested in each company be Rs. x.

S.I. = ${\text"Principal × Rate × Time"/100$

According to the question,

${x × 15 × 5}/100 - {x × 12 × 4}/100$ = 1350

${75x}/100 - {48x}/100$ = 1350

${27x}/100$ = 1350

$x = {1350 × 100}/27$ = Rs. 5000

Using Rule 13

Here, $P_1 = Rs. P, R_1 = 12%, T_1$ = 4 years

$P_2 = Rs. P, R_2 = 15%, T_2$ = 5 years

S.I. = Rs. 1350

S.I.= ${P_2R_2T_2 - P_1R_1T_1}/100$

1350 = ${P × 15 × 5 - P × 12 × 4}/100$

135000 = 75 P - 48P

135000 = 75 P

P = Rs. 5000