UPSC Insta–DART (Daily Aptitude and Reasoning Test) 12 Sep 2024
Kartavya Desk Staff
Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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• Question 1 of 5 1. Question Rashmi invested a sum of Rs. 1000 in a company. The company pays 10% interest per year. The company pays simple interest and the interest is added to the capital after a period of 5 years. What shall be the amount drawn by Rashmi if he withdraws his investment after 6 years? a) Rs. 1600 b) Rs. 1500 c) Rs. 1700 d) Rs. 1650 Correct Answer: Option (d) Explanation: Principal = Rs. 1000 Interest = 10% Interest for first five years = PRT/100 = 1000 × 10 × 5/100 = Rs. 500. This amount is reinvested after 5 years period. So, Principal after 5 years = Rs. 1000 + Rs. 500 = Rs. 1500. Interest for 6th year = 1500 × 10 × 1 /100 = Rs. 150. Total amount received after 6 years = Rs. 1500 + Rs. 150 = Rs. 1650 Hence, option (d) is the correct answer. Incorrect Answer: Option (d) Explanation: Principal = Rs. 1000 Interest = 10% Interest for first five years = PRT/100 = 1000 × 10 × 5/100 = Rs. 500. This amount is reinvested after 5 years period. So, Principal after 5 years = Rs. 1000 + Rs. 500 = Rs. 1500. Interest for 6th year = 1500 × 10 × 1 /100 = Rs. 150. Total amount received after 6 years = Rs. 1500 + Rs. 150 = Rs. 1650 Hence, option (d) is the correct answer.
#### 1. Question
Rashmi invested a sum of Rs. 1000 in a company. The company pays 10% interest per year. The company pays simple interest and the interest is added to the capital after a period of 5 years. What shall be the amount drawn by Rashmi if he withdraws his investment after 6 years?
• a) Rs. 1600
• b) Rs. 1500
• c) Rs. 1700
• d) Rs. 1650
Answer: Option (d)
Explanation:
Principal = Rs. 1000
Interest = 10%
Interest for first five years = PRT/100 = 1000 × 10 × 5/100 = Rs. 500.
This amount is reinvested after 5 years period.
So, Principal after 5 years = Rs. 1000 + Rs. 500 = Rs. 1500.
Interest for 6th year = 1500 × 10 × 1 /100 = Rs. 150.
Total amount received after 6 years = Rs. 1500 + Rs. 150 = Rs. 1650
Hence, option (d) is the correct answer.
Answer: Option (d)
Explanation:
Principal = Rs. 1000
Interest = 10%
Interest for first five years = PRT/100 = 1000 × 10 × 5/100 = Rs. 500.
This amount is reinvested after 5 years period.
So, Principal after 5 years = Rs. 1000 + Rs. 500 = Rs. 1500.
Interest for 6th year = 1500 × 10 × 1 /100 = Rs. 150.
Total amount received after 6 years = Rs. 1500 + Rs. 150 = Rs. 1650
Hence, option (d) is the correct answer.
• Question 2 of 5 2. Question Two statements S1 and S2 are given below followed by a question: S1: The difference between Compound Interest and Simple Interest at the same rate of interest for two years is Rs. 43.20. Simple Interest at the end of five years is Rs.3600. S2: The difference between Compound Interest and Simple Interest at the same rate of interest on Rs.12000 for 3 years is Rs.132.19. Question: What is the rate of Compound Interest per annum on a sum of money compounded annually? Which one of the following is correct in respect of the above statements and the Question? a) Either statement alone sufficient to answer the question b) Either statement alone not sufficient to answer the question c) Both the Statements 1 and 2 are required to answer the question. d) Both the Statements 1 and 2 are not sufficient to answer the question. Correct Answer: Option (a) Explanation: S1: Required rate of interest = (Difference between CI and SI / SI in one year) × 100 = [43.20 / (3600/5)] × 100 = 60% Hence, statement 1 alone is sufficient to answer the question. S2: Let S (in Rs.) be the sum invested and ‘r’ be the rate of interest. Difference between CI and SI = S × r2 132.19 = 12000 × r2 From above we can calculate value of r. Hence statement 2 alone sufficient to answer the question. Therefore Option (a) is correct answer. Incorrect Answer: Option (a) Explanation: S1: Required rate of interest = (Difference between CI and SI / SI in one year) × 100 = [43.20 / (3600/5)] × 100 = 60% Hence, statement 1 alone is sufficient to answer the question. S2: Let S (in Rs.) be the sum invested and ‘r’ be the rate of interest. Difference between CI and SI = S × r2 132.19 = 12000 × r2 From above we can calculate value of r. Hence statement 2 alone sufficient to answer the question. Therefore Option (a) is correct answer.
#### 2. Question
Two statements S1 and S2 are given below followed by a question:
S1: The difference between Compound Interest and Simple Interest at the same rate of interest for two years is Rs. 43.20. Simple Interest at the end of five years is Rs.3600.
S2: The difference between Compound Interest and Simple Interest at the same rate of interest on Rs.12000 for 3 years is Rs.132.19.
Question: What is the rate of Compound Interest per annum on a sum of money compounded annually?
Which one of the following is correct in respect of the above statements and the Question?
• a) Either statement alone sufficient to answer the question
• b) Either statement alone not sufficient to answer the question
• c) Both the Statements 1 and 2 are required to answer the question.
• d) Both the Statements 1 and 2 are not sufficient to answer the question.
Answer: Option (a)
Explanation:
S1: Required rate of interest
= (Difference between CI and SI / SI in one year) × 100
= [43.20 / (3600/5)] × 100 = 60%
Hence, statement 1 alone is sufficient to answer the question.
S2: Let S (in Rs.) be the sum invested and ‘r’ be the rate of interest.
Difference between CI and SI = S × r2
132.19 = 12000 × r2
From above we can calculate value of r. Hence statement 2 alone sufficient to answer the question. Therefore Option (a) is correct answer.
Answer: Option (a)
Explanation:
S1: Required rate of interest
= (Difference between CI and SI / SI in one year) × 100
= [43.20 / (3600/5)] × 100 = 60%
Hence, statement 1 alone is sufficient to answer the question.
S2: Let S (in Rs.) be the sum invested and ‘r’ be the rate of interest.
Difference between CI and SI = S × r2
132.19 = 12000 × r2
From above we can calculate value of r. Hence statement 2 alone sufficient to answer the question. Therefore Option (a) is correct answer.
• Question 3 of 5 3. Question A investment company offers its customers two schemes. Under Scheme A, it pays a simple interest at the rate of 11% p.a. whereas under scheme B it pays an interest of 10% compounded half yearly. Which scheme is better for a person who intends to invest the amount for one year only? a) Scheme A b) Scheme B c) Both give the same return d) Cannot be determined Correct Answer: Option (a) Explanation: Let the amount invested be P. Scheme A: Interest rate = 11% S.I. Simple interest for one year = PRT/100 =0.11P Scheme B: Interest rate = 10% compounded half yearly Interest rate for six months = 10/2 = 5% Amount after 1 year = P(1 + r/100)n = P(1+5/100)2 = P ×1.05 ×1.05 = 1.1025P So, Compound interest for one year = 1.1025 P – P = 0.1025P Hence, Scheme A is better for one year period. Option (a) is the correct answer. Incorrect Answer: Option (a) Explanation: Let the amount invested be P. Scheme A: Interest rate = 11% S.I. Simple interest for one year = PRT/100 =0.11P Scheme B: Interest rate = 10% compounded half yearly Interest rate for six months = 10/2 = 5% Amount after 1 year = P(1 + r/100)n = P(1+5/100)2 = P ×1.05 ×1.05 = 1.1025P So, Compound interest for one year = 1.1025 P – P = 0.1025P Hence, Scheme A is better for one year period. Option (a) is the correct answer.
#### 3. Question
A investment company offers its customers two schemes. Under Scheme A, it pays a simple interest at the rate of 11% p.a. whereas under scheme B it pays an interest of 10% compounded half yearly. Which scheme is better for a person who intends to invest the amount for one year only?
• a) Scheme A
• b) Scheme B
• c) Both give the same return
• d) Cannot be determined
Answer: Option (a)
Explanation:
Let the amount invested be P.
Scheme A: Interest rate = 11% S.I.
Simple interest for one year = PRT/100 =0.11P
Scheme B: Interest rate = 10% compounded half yearly
Interest rate for six months = 10/2 = 5%
Amount after 1 year = P(1 + r/100)n = P(1+5/100)2 = P ×1.05 ×1.05 = 1.1025P
So, Compound interest for one year = 1.1025 P – P = 0.1025P
Hence, Scheme A is better for one year period.
Option (a) is the correct answer.
Answer: Option (a)
Explanation:
Let the amount invested be P.
Scheme A: Interest rate = 11% S.I.
Simple interest for one year = PRT/100 =0.11P
Scheme B: Interest rate = 10% compounded half yearly
Interest rate for six months = 10/2 = 5%
Amount after 1 year = P(1 + r/100)n = P(1+5/100)2 = P ×1.05 ×1.05 = 1.1025P
So, Compound interest for one year = 1.1025 P – P = 0.1025P
Hence, Scheme A is better for one year period.
Option (a) is the correct answer.
• Question 4 of 5 4. Question Manish and Rituraj invested Rs. 12000 and Rs. 16000 in a business. After four months Manish and Rituraj both added Rs. 4000 in their initial investment. At the end of one year the total profit was Rs. 172500, if Manish and Rituraj invested their profit share on compound interest at the rate of 20% and 10% respectively then find difference between interests got by both at the end of two years? a) Rs.10250 b) Rs.11520 c) Rs.12210 d) Rs.13110 Correct Answer: Option (d) Explanation: Ratio of profit of Manish and Rituraj = [(12000 × 4)+ (12000 + 4000) × 8] : [(16000 × 4) + (16000 + 4000)× 8] = 17600 : 224000 = 11 : 14 Profit share of manish = 172500× 11/25 = Rs.75900 Profit share of Rituraj =172500× 14/25 = Rs. 96600 Equivalent CI of two year at the rate of 20% = 20+20+ (20× 20)/100 = 44% Equivalent CI of two year at 10% =10+10+ (10×10)/100 = 21% Required difference between interest = (75900× 44/100) – (96600× 21/100) = Rs.13110 Hence, option (d) is the correct answer. Incorrect Answer: Option (d) Explanation: Ratio of profit of Manish and Rituraj = [(12000 × 4)+ (12000 + 4000) × 8] : [(16000 × 4) + (16000 + 4000)× 8] = 17600 : 224000 = 11 : 14 Profit share of manish = 172500× 11/25 = Rs.75900 Profit share of Rituraj =172500× 14/25 = Rs. 96600 Equivalent CI of two year at the rate of 20% = 20+20+ (20× 20)/100 = 44% Equivalent CI of two year at 10% =10+10+ (10×10)/100 = 21% Required difference between interest = (75900× 44/100) – (96600× 21/100) = Rs.13110 Hence, option (d) is the correct answer.
#### 4. Question
Manish and Rituraj invested Rs. 12000 and Rs. 16000 in a business. After four months Manish and Rituraj both added Rs. 4000 in their initial investment. At the end of one year the total profit was Rs. 172500, if Manish and Rituraj invested their profit share on compound interest at the rate of 20% and 10% respectively then find difference between interests got by both at the end of two years?
• a) Rs.10250
• b) Rs.11520
• c) Rs.12210
• d) Rs.13110
Answer: Option (d)
Explanation:
Ratio of profit of Manish and Rituraj
= [(12000 × 4)+ (12000 + 4000) × 8] : [(16000 × 4) + (16000 + 4000)× 8]
= 17600 : 224000 = 11 : 14
Profit share of manish = 172500× 11/25 = Rs.75900
Profit share of Rituraj =172500× 14/25 = Rs. 96600
Equivalent CI of two year at the rate of 20%
= 20+20+ (20× 20)/100 = 44%
Equivalent CI of two year at 10%
=10+10+ (10×10)/100 = 21%
Required difference between interest
= (75900× 44/100) – (96600× 21/100) = Rs.13110 Hence, option (d) is the correct answer.
Answer: Option (d)
Explanation:
Ratio of profit of Manish and Rituraj
= [(12000 × 4)+ (12000 + 4000) × 8] : [(16000 × 4) + (16000 + 4000)× 8]
= 17600 : 224000 = 11 : 14
Profit share of manish = 172500× 11/25 = Rs.75900
Profit share of Rituraj =172500× 14/25 = Rs. 96600
Equivalent CI of two year at the rate of 20%
= 20+20+ (20× 20)/100 = 44%
Equivalent CI of two year at 10%
=10+10+ (10×10)/100 = 21%
Required difference between interest
= (75900× 44/100) – (96600× 21/100) = Rs.13110 Hence, option (d) is the correct answer.
• Question 5 of 5 5. Question On Rs. 3500 invested at a simple interest rate of 7 per cent per annum, Rs. 735 is obtained as interest in certain years. In order to earn Rs. 1275 as interest on Rs. 5000 in the same number of years, what should be the rate of simple interest? a) 7.5% b) 8.5% c) 9.25% d) 10.15% Correct Answer: Option (b) Explanation: From the given data, 3500×7×T/100=735 (Interest =PRT/100) => T =735/245=3 years Now, in the second case The interest per year = 1275/3=425 => 5000×1x R/100=425 => R = 8.5% Incorrect Answer: Option (b) Explanation: From the given data, 3500×7×T/100=735 (Interest =PRT/100) => T =735/245=3 years Now, in the second case The interest per year = 1275/3=425 => 5000×1x R/100=425 => R = 8.5%
#### 5. Question
On Rs. 3500 invested at a simple interest rate of 7 per cent per annum, Rs. 735 is obtained as interest in certain years. In order to earn Rs. 1275 as interest on Rs. 5000 in the same number of years, what should be the rate of simple interest?
Answer: Option (b)
Explanation:
From the given data, 3500×7×T/100=735 (Interest =PRT/100)
=> T =735/245=3 years
Now, in the second case
The interest per year = 1275/3=425
=> 5000×1x R/100=425
=> R = 8.5%
Answer: Option (b)
Explanation:
From the given data, 3500×7×T/100=735 (Interest =PRT/100)
=> T =735/245=3 years
Now, in the second case
The interest per year = 1275/3=425
=> 5000×1x R/100=425
=> R = 8.5%
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