type 1 basic simple interest using formula Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on simple interest topic of quantitative aptitude
(a) 3%
(b) 2.5%
(c) 5%
(d) 4%
The correct answers to the above question in:
Answer: (d)
Principal + S.I. for $5/2$ years = Rs.1012 ...(i)
Principal + S.I. for 4 years = Rs.1067.20 ...(ii)
Subtracting equation (i) from (ii)
S.I. for $3/2$ years = Rs.55.20
S.I. for $5/2$ years
= $55.20 × 2/3 × 5/2$ = Rs.92
Principal
= Rs.(1012 - 92) = Rs.920
Rate = ${92 × 100}/{920 × 5/2}$
= ${2 × 92 × 100}/{920 × 5}$ = 4%
Using Rule 12,
R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100
= $({1012 - 1067.20}/{1067.20 × 5/2 - 1012 × 4}) × 100$
= ${- 55.2}/({2668 - 4048}) × 100$
= ${- 55.2}/{- 1380} × 100$ = 4%
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Read more basic problems using formula Based Quantitative Aptitude Questions and Answers
Question : 1
A person borrows Rs.5,000 for 2 years at 4% per annum simple interest. He immediately lends it to another person at 6$1/4$% per annum simple interest for 2 years. His gain in the transaction is
a) Rs.450
b) Rs.112.50
c) Rs.150
d) Rs.225
Answer »Answer: (d)
Using Rule 1,
Case I :
S.I. = ${5000 × 2 × 4}/100$ = Rs.400
Case II :
S.I. = ${5000 × 25 × 2}/{100 × 4}$ = Rs.625
Gain = Rs.(625 - 400) = Rs.225
Question : 2
In how many years will a sum of Rs.3,000 yield a simple interest of Rs.1,080 at 12% per annum ?
a) 2$1/2$ years
b) 3 years
c) 3$1/2$ years
d) 2 years
Answer »Answer: (b)
Using Rule 1,
Time = ${SI × 100}/{\text"Principal × Rate"$
= ${1080 × 100}/{3000 × 12} = 3$ years
Question : 3
A sum of money amounts to Rs.850 in 3 years and to Rs.925 in 4 years at some rate of simple interest. The sum is :
a) Rs.600
b) Rs.550
c) Rs.700
d) Rs.625
Answer »Answer: (d)
Interest for 1 year
= Rs.(925 - 850) = Rs.75
If a sum becomes $a_1$ in $t_1$ years and $a_2$ in $t_2$ years then rate of interest
= ${100(a_2 - a_1)}/({a_1t_2 - a_2t_1})%$
= ${100(925 - 850)}/{850 × 4 - 3 × 925} = 7500/625$ = 12%
Principal = ${SI × 100}/{\text"Time × Rate"$
= ${75 × 100}/{1 × 12}$ = Rs.625
Using Rule 12,
P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$
= ${925 × 3 - 850 × 4}/{3 - 4}$
= ${2775 - 3400}/{-1}$
= ${- 625}/{- 1}$ = Rs.625
Question : 4
A man lent Rs.60,000, partly at 5% and the rest at 4% simple interest. If the total annual interest is Rs.2560, the money lent at 4% was
a) Rs.44000
b) Rs.40000
c) Rs.45000
d) Rs.30000
Answer »Answer: (a)
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 the amount lent at 4% be x
Amount lent at 5% = (60000 - x )
According to the question,
${(60000 - x) × 5 × 1}/100 + {x × 4 × 1}/100$ = 2560
300000 - 5x + 4x = 256000
x = 300000 - 256000 = Rs.44000
Question : 5
A sum of money lent out at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :
a) Rs.600
b) Rs.500
c) Rs.710
d) Rs.700
Answer »Answer: (a)
Principal + SI for 2 years = Rs.720 .... (i)
Principal + SI for 7 years = Rs.1020 .....(ii)
Subtracting equation (i) from (ii) get,
SI for 5 years
= Rs.(1020 - 720) = Rs.300
SI for 2 years
= Rs.300 × $2/5$ = Rs.120
Principal = Rs.(720 - 120) = Rs.600
Using Rule 12,
P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$
= $({1020 × 2 - 720 × 7}/{2 - 7})$
= $({2040 - 5040}/{- 5})$
= ${- 3000}/{- 5}$ = Rs.600
Question : 6
A sum of money amounts to Rs.5,200 in 5 years and to Rs.5,680 in 7 years at simple interest. The rate of interest per annum is
a) 4%
b) 3%
c) 6%
d) 5%
Answer »Answer: (c)
P + S.I. for 5 years = 5200 ..(i)
P + SI for 7 years = 5680 ...(ii)
On subtracting equation (i) from (ii),
SI for 2 years = 480
SI for 1 year = Rs.240
From equation (i),
P + 5 × 240 = 5200
P = 5200 - 1200 = Rs.4000
R = ${SI × 100}/{T × P}$
= ${240 × 100}/{1 × 4000}$ = 6%
Using Rule 12If certain sum P amounts to Rs. $A_1$ in $t_1$ years at rate of R% and the same sum amounts to Rs. $A_2$ in $t_2$ years at same rate of interest R%. Then,(i) R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100(ii) P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$
R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100
= $({5200 - 5680}/{5680 × 5 - 5200 × 7}) × 100$
= ${- 480}/{28400 - 36400}$ × 100
= ${- 480}/{- 8000} × 100$ = 6%
simple interest Shortcuts and Techniques with Examples
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type 1 basic simple interest using formula
Defination & Shortcuts … -
type 2 increase or decrease in interest rate
Defination & Shortcuts … -
type 3 money multiples in ‘n’ years
Defination & Shortcuts … -
type 4 difference & equality of si rate & years
Defination & Shortcuts … -
type 5 si on ‘n’ years & ‘x/y ‘of sum
Defination & Shortcuts … -
type 6 si with ratios
Defination & Shortcuts …
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