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

Answer: (b)

Using Rule 1,

Let first part be x and second part be(1750 –x )

According to the question,

x × $8/100 = (1750 - x ) × 6/100$

8x + 6x = 1750 × 6

14x = 1750 × 6

$x = {1750 × 6}/14$ = Rs.750

Interest = 8% of 750

= 750 × $8/100 = Rs.60

Answer: (d)

Let the sum lent be x.

${x × 7.5 × 5}/100 - {x × 7.5 × 4}/100 = 150$

${x × 7.5 × 1}/100$ = 150

$x = {150 × 100}/{7.5}$ = Rs.2000

Using Rule 13,

Here, $P_1 = P, R_1 = 7.5%, T_1$ = 4 years.

$P_2 = P, R_2 = 7.5%, T_2$ = 5 years.

S.I. = Rs.150

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

150 = ${P × 7.5 × 5 - P × 7.5 × 4}/100$

15000 = 7.5P

P = $15000/{7.5}$

P = $150000/75$ = Rs.2000

Answer: (d)

Using Rule 1,

Let the principal be x.

Time = $\text"SI × 100"/\text"Principal × Rate"$

= ${x × 100 × 3}/{x × 50}$ = 6 years

Answer: (d)

$\text"Simple interest"/ \text"Principal" = 1/9$

If the annual rate of interest be r%, then

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

$r = 1/9 × 100/r$

$r^2 = 100/9$

r = $√{100/9} = 10/3 = 3{1}/3$%

Using Rule 5,

Here, n = $1/9$, R = T

RT = n × 100

$R^2 = 1/9 × 100 = 100/9$

R = $√{100/9} = 10/3 = 3{1}/3$%

Answer: (d)

Let $r_1$, and $r_2$ be the required rate of interest

Then, ${13.50} = {1500 × 3 × r_1}/100$

– ${1500 × 3 × r_2}/100 = 4500/100(r_1 - r_2)$

$r_1 - r_2 = 135/450 = 27/90$

= $3/10$ = 0.3%

Using Rule 13,

$P_1 = Rs.1500, R_1 , T_1$ = 3 years.

$P_2 = Rs.1500, R_2 , T_2$ = 3 years.

S.I. = Rs.13.50

13.50 = ${1500 × R_2 × 3 - 1500 × R_1 × 3}/100$

$1350/100 = {4500(R_2 - R_1)}/100$

$R_2 - R_1 = 1350/4500 = 27/90$

= $3/10$ = 0.3%

Answer: (c)

Let the sum be x

${x × 5 × 15}/{100 × 12} - {x × 4 × 8}/{100 × 12}$ = 129

$x/{100 × 12}$(75 - 32) = 129

$x = {129 × 1200}/43$ = Rs.3600

Using Rule 13,

$P_1 = P, R_1 = 4%$

$T_1 = 8 months = 8/12$ years

$P_2 = P, R_2$ = 5%

$T_2 = 15 month = 15/12$ years

S.I. = Rs.129

129 = ${P × 5 × 15/12 - P × {4 × 8}/12}/100$

12900 = ${75P - 32P}/12$

12900 = ${43P}/12$

P = Rs.3600