Practice Si on n years - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A and B borrowed Rs. 3000 and Rs. 3200 respectively at the same rate of interest for 2$1/2$ years. If B paid Rs. 40 more interest than A, find the rate of interest.
(a)
(b)
(c)
(d)
Rate of interest = r % per annum
S.I. = ${\text"Principal × Rate × Time"/100$
According to the question,
${3200 × 5 × r}/{100 × 2} - {3000 × 5 × r}/200$ = 40
80r - 75r = 40
5r = 40 ⇒ r = $40/5$
= 8% per annum
Using Rule 13The difference between the S.I. for a certain sum $P_1$ deposited for time $T_1$ at $R_1$ rate of interest and another sum $P_2$ deposited for time $T_2$ at $R_2$ rate of interest isS.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$
Here, $P_1 = Rs.3000, R_1 = R, T_1 = 5/2$ years
$P_2 = Rs.3200, R_2 = R, T_2 = 5/2$ years
Difference S.I. = Rs.40
40 = ${3200 × R × 5/2 - 3000 × R × 5/2}/100$
4000 = 8000 R - 7500 R
R = 8%
Q-2) The simple interest on a sum after 4 years is $1/5$ of the sum. The rate of interest per annum is
(a)
(b)
(c)
(d)
Let Prinicpal = Rs.100
S.I. = $100 × 1/5$ = Rs.20
Rate = ${20 × 100}/{100 × 4}$ = 5%
Using Rule 5,
Here, n = $1/5$, T = 4 years.
R = ${n × 100}/T$
R = $1/5 × 100/4$
R = 5%
Q-3) On a certain sum, the simple interest at the end of 6$1/4$ years becomes $3/8$ of the sum. The rate of interest is
(a)
(b)
(c)
(d)
$\text"Interest"/ \text"Principal" = 3/8$
Rate = ${\text"SI" × 100}/\text"Principal × Time"$
= $3/8 × 100/{25/4}$
= $3/8 × 400/25$ = 6% per annum
Using Rule 5,
Here, n = $3/8$, T = $25/4$ years.
R = ${n × 100}/T$
= $3/8 × 100/{25/4}$ ⇒ R = 6%
Q-4) The simple interest on a sum for 5 years is one fourth of the sum. The rate of interest per annum is
(a)
(b)
(c)
(d)
$\text"Simple interest"/\text"Principal" = 1/4$
Rate = ${\text"SI" × 100}/\text"Principal × Time"$
= ${1 × 100}/{4 × 5} = 5%$ per annum
Using Rule 5,
Here, n = $1/4$, T = 5 years
R = ${n × 100}/T$
= $1/4 × 100/5$ = R = 5%
Q-5) Simple interest on a certain sum for 4 years is $12/25$ of the sum. The rate of interest is
(a)
(b)
(c)
(d)
Rate = ${\text"SI" × 100}/\text"Principal × Time"$
= $12/25 × 100/4$ = 12% per annum
Using Rule 5,
Here, n = $12/25$, T = 4 years.
R = ${n × 100}/T$
R = $12/25 × 100/4$
R = 12%
Q-6) The present worth of a bill due 7 months hence is Rs.1200 and if the bill were due at the end of 2$1/2$ years its present worth would be Rs.1016. The rate per cent 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
S.I. = ${\text"Principal × Rate × Time"/100$
1200 + ${1200 × 7 × r}/{12 × 100}$
= Amount (A)
1200 + 7r = A ...(i)
and, 1016 + ${1016 × 5 × r}/{2 × 100}$ = A
1016 + 25.4r = A ...(ii)
1016 + 25.4r = 1200 + 7r
25.4r - 7r = 1200 - 1016
18.4r = 184 ⇒ r = $184/{18.4}$
= 10% per annum
Q-7) Simple interest on a certain sum for 6 years is $9/25$ of the sum. The rate of interest is
(a)
(b)
(c)
(d)
Rate = ${\text"SI" × 100}/\text"Principal × Time"$
= $9/25 × 100/6$ = 6% per annum
Using Rule 5,
Here, n = $9/25$, T = 6 years.
R = ${n × 100}/T$
R = $9/25 × 100/6$
R = 6%
Q-8) In what time will the simple interest be $2/5$ of the principal at 8 per cent per annum?
(a)
(b)
(c)
(d)
Let the principal be x
Interest = $2/5$ x
Rate = 8% per annum
Time = ${\text"Interest" × 100}/\text"Principal × Rate"$
=${{2/5}x × 100}/{x × 8} = 40/8$ = 5 years
Using Rule 5If Simple Interest (S.I.) becomes 'n' times of principal i.e.S.I. = P × n then.RT = n × 100
Here, n = $2/5$ and R = 8%
RT = (n × 100)
T = ${n × 100}/R$
T = $2/5 × 100/8$ = 5 years
Q-9) At the rate of simple interest per annum, the interest on a certain sum of money for 10 years will be $2/5$th part of the amount, then the rate of simple interest is
(a)
(b)
(c)
(d)
Amount after 10 years
= P$(1 + {RT}/100)$ = P$(1 + {R × 10}/100)$
= Rs. P$(1 + R/10)$
Interest = Rs.P$(1 + R/10) × 2/5$
Rate= ${\text"SI" × 100}/\text"Principal × Time"$
R = ${P(1 + R/10) × 2/5 × 100}/{P × 10}$
R = 4$(1 + R/10)$
$R/4 = 1 + R/10$
$R/4 - R/10$ = 1
${5R - 2R}/20$ = 1
3R = 20
R = $20/3 = 6{3}2%$
Using Rule 5,
Here, S.I. = $2/5$ amount
S.I. = $2/5$ (P + S.I.)
S.I. = $2/5$ S.I. + $2/5$ P
$3/5$ S.I. = $2/5$ P
S.I. = $2/3$P
Now, n = $2/3$, T = 10 years.
R= ${n × 100}/T$
= $2/3 × 100/10$
= $20/3 = 6{2}/3%$
Q-10) The simple interest on a sum at x% for x years is x. What is the sum?
(a)
(b)
(c)
(d)
P = $\text"100 × SI"/\text"R × T"$
= $\text"100 × x"/\text"x × x"$ = $100/x$