type 3 money multiples in ‘n’ years Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Tier-II 2015]

The simple interest on a sum of money is $8/25$ of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annum is

a) 8

b) 5

c) 4

d) 6$1/4$

Answer: (a)

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.I. = ${\text"P × R × T"/100$
P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$
A = P + S.I. or S.I. = A - P

Rate = R% per annum

Time = $R/2$ years

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

R = $8/25 × 100/{R/2}$

$R^2 = {8 × 200}/25$ = 64

R = $√{64}$ = 8% per annum

Question : 2 [SSC CPO SI 2016]

A certain sum doubles in 7 years at simple interest. The same sum under the same interest rate will become 4 times in how many years.

a) 28

b) 14

c) 10

d) 21

Answer: (d)

Case I,

Interest = Principal

Rate = ${Interest × 100}/\text"Principal × Time"$

= $100/7%$ per annum

Case II,

Interest = 3 × Principal

Time = ${Interest × 100}/\text"Principal × Time"$

= ${3 × 100}/{100/7}$ = 3 × 7 = 21 years

Question : 3 [SSC CGL Tier-I 2016]

At what per cent of simple interest will a sum of money double itself in 15 years?

a) 6$2/3$%

b) 6$1/3$%

c) 6%

d) 6$1/2$%

Answer: (a)

Let principal be Rs.x.

Amount = Rs.2x

Interest = Rs.(2x - x) = Rs.x

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

= ${x × 100}/{x × 15} = 20/3$

= 6$2/3%$ per annum

Question : 4 [SSC CGL Prelim 2008]

A sum of money at a certain rate per annum of simple interest doubles in the 5 years and at a different rate becomes three times in 12 years. The lower rate of interest per annum is

a) 20%

b) 15%

c) 16$2/3$%

d) 15$3/4$%

Answer: (c)

The sum gets doubled in 5 years and tripled in 12 years.

Clearly rate of interest for 12 years will be lower.

Let Principal be x.

then, Rate = ${SI × 100}/\text"Principal × Time"$

= ${2x × 100}/{x × 12} = 50/3 = 16{2}/3%$

Using Rule 3,

$R_1 = {(2 - 1)}/5 × 100%$ = 20%

$R_2 = {(3 - 1)}/12 × 100% = 16{2}/3%$

Lower rate of interest =16$2/3%$

Question : 5 [SSC CGL Tier-I 2016]

The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is :

a) 40%

b) 30%

c) 55%

d) 50%

Answer: (d)

Principal = Rs.x (let)

Amount = Rs.5x

Interest = Rs.(5x - x) = Rs.4x

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

= ${4x × 100}/{x × 8}$ = 50% per annum

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