model 3 combination of si & ci Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

Difference of CI and SI for two years

= Rs.(954 - 900) = Rs.54

Sum= Difference in CI and SI × $(100/{Rate})^2$

Rate = ${2 × \text"Difference" × 100}/\text"Simple interest"$

= ${2 × 5400}/900 = 12%$

Sum = 54 × $(100/12)^2$

= $54 × 25/3 × 25/3$ = Rs.3750

Using Rule 10,

C.I. = Rs.954, S.I.=Rs.900, P=?

C.I.= S.I.$(1 + R/200)$

954 = 900$(1 + R/200)$

$954/900 = 1 + R/200$

$954/900 - 1 = R/200$

${954 - 900}/900 = R/200$

$54/9 = R/2$

R = 12%

Now S.I. = ${P × R × T}/100$

900 = ${P × 12 × 2}/100$

P = Rs.3750

Answer: (d)

C.I.= P$(1 + r/100)^t$ - P

2448 = P$[(1 + r/100)^t - 1]$

or 2448 = P$[(1 + 4/100)^2 - 1]$

2448 = P$[676/625 - 1]$

2448 = P$[51/625]$

P = ${2448 × 625}/51$ = Rs.30,000

S.I. = ${30000 × 4 × 2}/100$ = Rs.2400

Using Rule 10,

Here, C.I. = Rs.2448, R = 4%, S.I. = ?

C.I.= S.I.$(1 + R/200)$

2448 = S.I.$(1 + 4/200)$

2448 = S.I.$(1 + 1/50)$

2448 = S.I.$(51/50)$

S.I. = ${2448 × 50}/51$ = Rs.2400

Answer: (a)

Let the principal be Rs.P. For 4 years,

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

= ${P × 4 × 5}/100$ = Rs.$P/5$

C.I. = P$[(1 + R/100)^T - 1]$

= P$[(1 + 10/100)^4 - 1]$

= P$[(11/10)^4 - 1]$

= P$(14641/10000 - 1) = {4641P}/10000$

According to the question,

${4641P}/10000 - P/5$ = 26410

${4641P - 2000P}/10000$ = 2641

${2641P}/10000$ = 2641

P = Rs.10000

Answer: (b)

Compound interest = P $[(1 + R/100)^T - 1]$

410 = P$[(1 + 5/100)^2 - 1]$

410 = P$[(1 + 1/20)^2 - 1]$

410 = P$[(21/20)^2 - 1]$

410 = P$(441/400 - 1)$

410 = P$(41/400)$

P = ${410 × 400}/41$ = Rs.4000

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

= ${4000 × 2 × 5}/100$ = Rs.400

Using Rule 10,

Here, C.I. = Rs.410, R = 5%, S.I. = ?

C.I. = S.I.$(1 + R/200)$

410 = S.I.$(1 + 5/200)$

410 = S.I.$(205/200)$

S.I. = ${410 × 200}/205$ = Rs.400

Answer: (b)

C.I. = P$[(1 + R/100)^T - 1]$

2544 = P$[(1 + 12/100)^2 - 1]$

2544 = P$[(28/25)^2 - 1]$

2544 = P$(784/625 - 1)$

2544 = P$({784 - 625}/625)$

2544 = ${P × 159}/625$

P = ${2544 × 625}/159$ = Rs.10000

S.I. = ${P × R × T}/100$

= ${10000 × 2 × 12}/100$ = Rs.2400

Using Rule 10,

Here, C.I. = Rs.2544, R = 12%, S.I. = ?

C.I. = S.I.$(1 + R/200)$

2544 = S.I.$(1 + 12/200)$

2544 = S.I.$(212/200)$

S.I. = ${2544 × 200}/212$ = Rs.2400