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A sum of money doubles in 5 years at simple interest. Find the rate of interest.
1. 20%
2. 10%
3. 15%
4. 25%
Correct Answer - Option 1 : 20%GivenAmount = 2(principal)FormulaSimple interest = (p × r × t)/100Where p, r and t represents principal, rate of interest and timeCalculationSimple interest = Amount – Principal⇒ Rs. 2P – P⇒ P⇒ P = ( P × r × 5)/100⇒ r = 20 %Alternative methodIf a sum of money becomRead more
Correct Answer – Option 1 : 20%
Given
Amount = 2(principal)
Formula
Simple interest = (p × r × t)/100
Where p, r and t represents principal, rate of interest and time
Calculation
Simple interest = Amount – Principal
⇒ Rs. 2P – P
⇒ P
⇒ P = ( P × r × 5)/100
⇒ r = 20 %
Alternative method
If a sum of money becomes ‘a’ times in ‘t’ years at simple interest, then formula for calculating rate of interest will be as follows:
Rate of interest = 100(a – 1)/t
Solution:
a= 2, t = 5
Rate of interest = 100(2 – 1)/5
⇒ 20 %
See lessWhat total amount is to be paid on a sum of Rs. 12,000 for \(1 \frac{1}{2}\) years at 10% per annum compounded half yearly?
1. Rs. 13,891.50
2. Rs. 19,831.50
3. Rs. 31,918.50
4. Rs. 13,230.50
Correct Answer - Option 1 : Rs. 13,891.50Given:The sum = Rs 12,000Time = \(1 \frac{1}{2}\) yearsRate = 10% p.a.Formula used:A = P(1 + R/100)tHere, A, P, R and t are the Amount, Principal, Rate and time respectivelyConcept used:When compounded half-yearly then,Rate is half and time is doubledCalculatRead more
Correct Answer – Option 1 : Rs. 13,891.50
Given:
The sum = Rs 12,000
Time = \(1 \frac{1}{2}\) years
Rate = 10% p.a.
Formula used:
A = P(1 + R/100)t
Here, A, P, R and t are the Amount, Principal, Rate and time respectively
Concept used:
When compounded half-yearly then,
Rate is half and time is doubled
Calculation:
Rate = 10%/2 = 5% and Time = \(1 \frac{1}{2}\) × 2 = 3 half yearly
Now, A = P(1 + R/100)t
⇒ A = 12000(1 + 5/100)3
⇒ A = 12000 × 21/20 × 21/20 × 21/20
⇒ A = 13891.5
∴ The total amounts to be paid is Rs 13891.50
See lessThe simple interest on a sum after 4 years is \(\frac{1}{5}\) of the sum. The rate of interest per annum is:
1. 4%
2. 6%
3. 5%
4. 8%
Correct Answer - Option 3 : 5%Given:SI = 1/5 × PT = 4 yrFormula used:SI = P × R% × TCalculation:SI = P × R% × T⇒ 1/5 × P = P × R/100 × 4⇒ 20/4 = R⇒ R = 5%∴ The rate of interest per annum is 5%.
Correct Answer – Option 3 : 5%
Given:
SI = 1/5 × P
T = 4 yr
Formula used:
SI = P × R% × T
Calculation:
SI = P × R% × T
⇒ 1/5 × P = P × R/100 × 4
⇒ 20/4 = R
⇒ R = 5%
∴ The rate of interest per annum is 5%.
See lessWhat will be the sum on which the rate of interest is 4% per annum for the first 2 yr, 6% per annum for the next 4 yr and 8% per annum for the period beyond 6 yr. if the simple interest accrued by the sum for a total period of 9 yr is Rs. 4480?
1. 7200
2. 12400
3. 9220
4. 11800
5. 8000
Correct Answer - Option 5 : 8000GIVEN:For the first 2 years, r = 4% per annum, t = 2 yearsnext 4 years, r = 6% per annum, t = 4 yearsnext 3 years, r = 8% per annum, t = 3 years FORMULAE USED:SI = (p × r × t)/100CALCULATION: the simple interest for the first 2 years = (p × 4 × 2)/100 = 2p/25the simplRead more
Correct Answer – Option 5 : 8000
GIVEN:
For the first 2 years, r = 4% per annum, t = 2 years
next 4 years, r = 6% per annum, t = 4 years
next 3 years, r = 8% per annum, t = 3 years
FORMULAE USED:
SI = (p × r × t)/100
CALCULATION:
the simple interest for the first 2 years = (p × 4 × 2)/100 = 2p/25
the simple interest for the next 4 years = (p × 6 × 4)/100 = 6p/25
And then, for the
the simple interest for the next 3 years = (p × 8 × 3)/100 = 6p/25
⇒ Total interest = (2p/25) + (6p/25) + (6p/25) = 14p/25
So, 14p/25 = 4480
⇒ p = Rs. 8000
Hence, the principal amount is Rs. 8000
See lessA man borrows Rs.21630 on compound interest and return it in three equal year installments. Find the installment charge per year if the rate of 20/3% p.a?
1. Rs. 1000
2. Rs. 981
3. Rs. 1200
4. Rs. 2200
5. Rs.8192
Correct Answer - Option 5 : Rs.8192Given:Principal (P) = 21630, Rate (R) = 20/3%, Installment = 3Formula used:Instalment = \(\frac{x}{{{{(1 + \frac{R}{{100}})}^n}}}\)Calculation:Let, x be the equal instalmentTotal number of instalment is 3Accordingly, \(\frac{x}{{1 + \frac{{20}}{{300}}}} + \frac{x}{Read more
Correct Answer – Option 5 : Rs.8192
Given:
Principal (P) = 21630,
Rate (R) = 20/3%,
Installment = 3
Formula used:
Instalment = \(\frac{x}{{{{(1 + \frac{R}{{100}})}^n}}}\)
Calculation:
Let, x be the equal instalment
Total number of instalment is 3
Accordingly,
\(\frac{x}{{1 + \frac{{20}}{{300}}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^2}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^3}}} = 21630\)
⇒ \(\frac{{15x}}{{16}} + \frac{{225x}}{{256}} + \frac{{3375x}}{{4096}} = 21630\)
⇒ (3840x + 3600x + 3375x) = 4096 × 21630
⇒ 10815x = 4096 × 21630
⇒ x = (4096 × 21630)/10815
∴ Installment is 8192
See lessThe principal increases by 14% in 2 years at simple interest, what will be the compound interest earned (in Rs) on Rs10,000 in 3 years at the same rate?
1. Rs.2250.90
2. Rs.2250.43
3. Rs.2250
4. Rs.2350.43
Correct Answer - Option 2 : Rs.2250.43Given:Time (T) = 2 yearsTime (n) = 3 yearsFormula used:S.I. = (P × R × T)/100 A = P(1 + R/100)nWhere A → amountn → timeS.I. → Simple InterestP → PrincipalR → Rate T → TimeCalculations:Let the principal be Rs. P and the rate be R p.a.The principal after 2 years =Read more
Correct Answer – Option 2 : Rs.2250.43
Given:
Time (T) = 2 years
Time (n) = 3 years
Formula used:
S.I. = (P × R × T)/100
A = P(1 + R/100)n
Where A → amount
n → time
S.I. → Simple Interest
P → Principal
R → Rate
T → Time
Calculations:
Let the principal be Rs. P and the rate be R p.a.
The principal after 2 years = P + 14P/100
According to the question,
P + 14P/100 = P + (P × R × 2)/100
⇒ 1 + (14/100) = R/50
⇒ R = 50 × (14/100) = 7%
Now
A = 10000(1 + 7/100)3
⇒ A = 10000 × (107/100) × (107/100) × (107/100)
⇒ A = Rs.12250.43
Thus C.I. = 12250.43 – 10000 = Rs.2250.43
∴ The compound interest earned on Rs10,000 in 3 years is Rs.2250.43.
See lessA certain sum is invested under simple interest for 9 years at a certain rate of interest. Had the rate of interest been 1% more, the interest for 9 years would have been Rs. 234 more. Find the sum.
1. Rs. 3500
2. Rs. 2600
3. Rs. 2500
4. Rs. 3600
Correct Answer - Option 2 : Rs. 2600Given: A certain sum is invested under simple interest for 9 years at a certain rate of interest.Had the rate of interest been 1% more, the interest for 9 years would have been Rs. 234 more.Formula: S.I = PRT/100Where, P = PrincipalR = Rate of interestT = Time takRead more
Correct Answer – Option 2 : Rs. 2600
Given:
A certain sum is invested under simple interest for 9 years at a certain rate of interest.
Had the rate of interest been 1% more, the interest for 9 years would have been Rs. 234 more.
Formula:
S.I = PRT/100
Where, P = Principal
R = Rate of interest
T = Time taken
Calculation:
Let the sum be P and rate of interest be r
[(P × r × 9)/100] + 234 = [P × (r + 1) × 9]/100
⇒ 234 = P × (9/100)
⇒ P = 234 × (100/9)
⇒ P = Rs. 2600
∴ The sum is Rs. 2600
See lessFor 3 years, the difference between simple interest and compound interest is Rs. 616 at 8% per annum. Find the compound interest in 2 years at the same rate of interest at same sum.
1. Rs. 2240
2. Rs. 4150
3. Rs. 5200
4. Rs. 1250
Correct Answer - Option 3 : Rs. 5200Given:For 3 years, the difference between simple interest and compound interest = Rs. 616Rate = 8%For compound interest, time = 2 years.Concept used:C.I. = P{(1 + R/100 )T – 1}D = P × (R/100)2(300 + R)/100S.I. → Simple interestP → PrincipalT → TimeR → Rate%C.I. →Read more
Correct Answer – Option 3 : Rs. 5200
Given:
For 3 years, the difference between simple interest and compound interest = Rs. 616
Rate = 8%
For compound interest, time = 2 years.
Concept used:
C.I. = P{(1 + R/100 )T – 1}
D = P × (R/100)2(300 + R)/100
S.I. → Simple interest
P → Principal
T → Time
R → Rate%
C.I. → Compound interest
D → Difference between S.I. and C.I. for 3 years difference,
Calculations:
D = P × (R/100)2(300 + R)/100
⇒ 616 = P × (8/100)2(300 + 8)/100
⇒ 616 = P × (64/10000) × (308/100)
P = (616 × 10000 × 100)/(308 × 64)
⇒ Rs. 31,250
At the same sum,
C.I. = P{(1 + R/100 )T – 1}
⇒ 31250{(1 + 8/100)2 – 1}
⇒ 31250 × {(108/100) × (108/100) – 1}
⇒ 31250 × {(11664/10000) – 1}
⇒ 31250 × (1664/10000)
⇒ Rs. 5200
∴ The compound interest is Rs. 5200
See lessNina borrows Rs. 7500 at 10% p.a. She pays Rs. 2800 at end of year 1 and Rs. 1500 at end of year 2. How much amount should she pay at end of year 3 to clear all her dues?
1. Rs. 5509.5
2. Rs. 4560.5
3. Rs. 4944.5
4. Rs. 5204.5
Correct Answer - Option 3 : Rs. 4944.5Given:P = Rs. 7500R = 10%N = 3 YearsAmount paid back at end of year 1 = Rs. 2800Amount paid back at end of year 2 = Rs. 1500Formula used:A = P × {1 + (R / 100)}NWhere P = Principal amount, R = Rate of interest in %, N = Number of yearsA = P + ICalculation:AmountRead more
Correct Answer – Option 3 : Rs. 4944.5
Given:
P = Rs. 7500
R = 10%
N = 3 Years
Amount paid back at end of year 1 = Rs. 2800
Amount paid back at end of year 2 = Rs. 1500
Formula used:
A = P × {1 + (R / 100)}N
Where P = Principal amount, R = Rate of interest in %, N = Number of years
A = P + I
Calculation:
Amount to be paid at end of 1st year = 7500 × {1 + (10 / 100)}
⇒ A = 8250
She pays Rs. 2800 at end of 1st year
⇒ Amount left = 8250 – 2800
⇒ Amount left = 5450
Amount at end of 2nd year = 5450 × {1 + (10 / 100)}
⇒ Amount at end of 2nd year = 5995
She paid Rs. 1500 at the end of 2nd year
⇒ Amount left to pay = (5995 – 1500)
⇒ Amount left to pay at end of 2nd year = Rs. 4495
Amount at end of 3rd year = 4495 × {1 + (10 / 100)}
⇒ Amount at end of 3rd year = 4944.5
∴ At the end of year 3 she need to pay Rs. 4944.5 to clear all her dues.
See lessCalculate total interest earned if an amount of INR 8000 is divided into two parts. 40% of the amount is compounded at a 20% p.a. rate of interest for two years and 60% earns simple interest at the same rate for the same years.
1. Rs. 3328
2. Rs. 4208
3. Rs. 3764
4. Rs. 4586
Correct Answer - Option 1 : Rs. 3328Given:Rate of interest = 20%Years = 2Principal amount = 8000Formula used:Simple interest: (P × R × T) / 100Compound interest: Amount = P (1 + (R/100))nWhere, n = Number of years, P = Principal Amount, R = Rate of Interest, A = AmountCalculations:Here, 40% of amounRead more
Correct Answer – Option 1 : Rs. 3328
Given:
Rate of interest = 20%
Years = 2
Principal amount = 8000
Formula used:
Simple interest: (P × R × T) / 100
Compound interest: Amount = P (1 + (R/100))n
Where, n = Number of years, P = Principal Amount, R = Rate of Interest, A = Amount
Calculations:
Here, 40% of amount is compounded
⇒ P for C.I. = (40 / 100) × 8000
⇒ P for C.I. = 3200
⇒ 3200 × (1 + (20 / 100))2
⇒ 3200 × (6 / 5)2
⇒ 3200 × 36 / 25
⇒ 4608
⇒ Interest earned = 4608 – 3200
⇒ I = 1408
Now,
⇒ 60% of amount = 8000 – 3200
⇒ P for S.I. = 4800
⇒ 4800 × 20 × 2 / 100
⇒ I = 1920
∴ Total interest earned is Rs. 3328
See less