model 5 ci with instalments Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Using Rule 1,

Let the income of company in 2010 be Rs.P

According to the question,

A = P$(1 + R/100)^T$

2664000 = P$(1 + 20/100)^2$

2664000 = P$(1 + 1/5)^2$

2664000 = P × $(6/5)^2$

P = ${2664000 × 5 × 5}/{6 × 6}$ = Rs.1850000

Answer: (d)

Using Rule 9(i),

Let each instalment be x.

$x/(1 + 5/100) + x/(1 + 5/100)^2 = 12300$

${20x}/21 + (20/21)^2x = 12300$

${20x}/21(1 + 20/21)$ = 12300

${20x}/21 × 41/21 × x = 12300$

$x = {12300 × 21 × 21}/{20 × 41}$ ⇒ x = 6615

Answer: (d)

Let principal (present worth) for first year be $P_1$ and that for two years be $P_2$.

16224 = $P_1(1 + 4/100)$

16224 = $P_1(1 + 1/25) = {26P_1}/25$

$P_1 = {16224 × 25}/26$ = Rs.15600

Again,

$16224 = P_2(1 + 4/100)^2$

16224 = $P_2(26/25)^2 = {676P_2}/625$

$P_2 = {16224 × 625}/676$ = 15000

Cash value of the scooter

= Rs.(16224 + 15600 + 15000) = Rs.46824

Answer: (d)

Using Rule 9(i),

Let the value of each instalment be Rs.x

Principal = Present worth of Rs.x due 1 year hence, present worth of Rs. x due 2 years hence

210 = $x/(1 + R/100) + x/(1 + R/100)^2$

210 = $x/(1 + 10/100) + x/(1 + 10/100)^2$

210 = $x/{1 + 1/10} + x/(1 + 1/10)^2$

210 = $x/{11/10} + x/(11/10)^2$

210 = ${10x}/11 + {100x}/121$

210 = ${110x + 100x}/121$

210 × 121 = 210 x

$x = {210 × 121}/210$ = Rs.121

Answer: (c)

Let the annual instalment be x

A = P$(1 + R/T)^T$

$x = P_1(1 + 25/200)$

$x = P_1 × 9/8$

$P_1 = 8/9x$

Similarly, $P_2 = 64/81x$

$P_1 + P_2$ = 6800

$8/9x + 64/81x$ = 6800

${72x + 64x}/81 = 6800$

${136x}/81 = 6800$

$x = {6800 × 81}/136$ = Rs.4050

Using Rule 9(i),

Here, P = Rs.6800, R = $25/2$%, n = 2

Each instalment

= $p/{(100/{100 + r}) + (100/{100 + r})^2$

= $6800/{(100/{100 +{25/2}}) + (100/{100 + {25/2}})^2$

= $6800/{200/225 + (200/225)^2}$

= $6800/{200/225(1 + {200/225})}$

= ${6800 × 225 × 225}/{200 × 425}$ = Rs.4050

Answer: (b)

A = Rs.2550

R = 4% per annum

n = 2 years

Let each of the two equal instalments be x

Present worth = $\text"Instalment"/(1 + r/100)^n$

$P_1 = x/(1 + 4/100)^1 = x/{1 + 1/25} = x/{26/25}$

or $P_1 = 25/26x$

Similarly,

$P_2 = (25/26)^2x = 625/676x$

$P_1 + P_2$ = A

$25/26x + 625/676x$ = 2550

${(650 + 625)x}/676 = 2550$

$1275/676x = 2550$

x = 2550 $× 676/1275$ ⇒ x = Rs.1352

Here, P = Rs.2550, n = 2, r = 4%

Each instalment

= $p/{(100/{100 + r}) + (100/{100 + r})^2$

= $2550/{(100/{100 + 4}) + (100/{100 + 4})^2$

= $2550/{100/104 + (100/104)^2}$

= $2550/{100/104(1 + 100/104)}$

= $2550/{100/104 (204/104)}$

= ${2550 × 104 × 104}/20400 $= Rs.1352