Practice Money multiples in n years - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) 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)
(b)
(c)
(d)
Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.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
Q-2) 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)
(b)
(c)
(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
Q-3) At what rate per cent per annum will the simple interest on a sum of money be $2/5$ of the amount in 10 years ?
(a)
(b)
(c)
(d)
Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.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
Let P be the principal and R% rate of interest.
S.I. = ${\text"PR" × 10}/100 = \text"PR"/10$
According to the question,
${PR}/10 = (P + {PR}/10) × 2/5$
$R/10 = (1 + R/10) × 2/5$
$R/10 = 2/5 + R/25$
$R/10 - R/25 = 2/5$
${5R - 2R}/50 = 2/5$
${3R}/50 = 2/5$
R = ${50 × 2}/{3 × 5} = 20/3 = 6{2}/3$%
Q-4) The rate of simple interest per annum at which a sum of money doubles itself in 16$2/3$ years is
(a)
(b)
(c)
(d)
According to the question,
Principal = Rs.x.
Interest = Rs.x.
Time = $50/3$ years
Rate = ${Interest × 100}/\text"Principal × Time"$
= ${x × 100}/{x × {50/3}}$
= ${100 × 3}/50$ = 6% per annum
Q-5) A sum of money becomes $41/40$ of itself in $1/4$ years at a certain rate of simple interest. The rate of interest per annum is
(a)
(b)
(c)
(d)
Let the principal be Re.1
S.I. = $41/40 - 1 = 1/40$
Now, rate = ${\text"Interest" ×100}/{\text"Principal × Time"}$
= ${1/40 × 100}/{1 × 1/4} = {100 × 4}/40$ = 10%
Using Rule 3,
R = ${(41/40 - 1) × 100%}/{1/4}$
= $1/40 × 4 × 100%$ = 10%
Q-6) 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)
(b)
(c)
(d)
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$2/3%$
Q-7) The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is :
(a)
(b)
(c)
(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
Q-8) If a sum of money doubles itself in 8 years, then the interest rate in percentage is
(a)
(b)
(c)
(d)
Let principal be Rs. x.
Amount = Rs.2x
Interest = Rs.(2x - x) = Rs.x
Rate = ${S.I. × 100}/\text"Principal × Time"$
= ${x × 100}/{x × 8} = 25/2$
= 12$1/2%$ per annum
Q-9) If a sum of money at simple interest doubles in 12 years, the rate of interest per annum is
(a)
(b)
(c)
(d)
Let the principal be x.
Amount = 2x
Interest = (2x - x) = x
Rate = ${S.I. × 100}/\text"Principal × Time"$
= ${x × 100}/{x × 12} = 25/3 = 8{1}/3%$
Using Rule 3,
R = ${(2 - 1)}/12 × 100%$
R = $25/3% = 8{1}/3$%
Q-10) A sum amounts to double in 8 years by simple interest. Then the rate of simple interest per annum is
(a)
(b)
(c)
(d)
Principal = Rs.x
Amount = Rs.2x
Interest = 2x - x = Rs.x
Rate = ${SI × 100}/\text"Principal × Time"$
= ${x × 100}/{x × 8} = 25/2$ = 12.5 % per annum
Using Rule 3,
R % = ${(n - 1)}/T × 100%$
= ${(2 - 1)}/8 × 100%$ = 12.5%