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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.
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Question 1 of 5
1. Question
33 men can do a job in 30 days. If 44 men started the job together and after every day of the work, one person leaves. What is the minimum number of days required to complete the whole work?
Correct
Your Answer :C
If 33 men can do a job in 30 days, then there are 33 X 30 = 990 pieces of job.
If 44 pieces of work is done on the first day, then 43 pieces will be done on second day. Cumulatively, 44+43+42+………. = 990 days. This is the problem of sum of series with starting number as a = 44 and difference d = -1.
From the formula for Sum of the series S = n/2( 2a + (n-1) d) 990 = n/2 (2 × 44 + (n-1) × -1
1980 = n (89 – n) 1980 = 89n – n2 n^2 – 89n + 1980=0 Solving quadratic equation, n = 44 or 45. Therefore, minimum number of days required is 44 days.
Incorrect
Your Answer :C
If 33 men can do a job in 30 days, then there are 33 X 30 = 990 pieces of job.
If 44 pieces of work is done on the first day, then 43 pieces will be done on second day. Cumulatively, 44+43+42+………. = 990 days. This is the problem of sum of series with starting number as a = 44 and difference d = -1.
From the formula for Sum of the series S = n/2( 2a + (n-1) d) 990 = n/2 (2 × 44 + (n-1) × -1
1980 = n (89 – n) 1980 = 89n – n2 n^2 – 89n + 1980=0 Solving quadratic equation, n = 44 or 45. Therefore, minimum number of days required is 44 days.
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Question 2 of 5
2. Question
If a leap year begins with Sunday, which of the following days in that year will come for 53 times?
- Sunday
- Monday
- Tuesday
- Saturday
Correct
Your Answer : A
In a leap year, there are 366 days. There will be 52 complete weeks (52*7=364 days) and 2 days are left. So, in a cycle, 1st and 2nd day of that year will repeat as 365th and 366th days of that year.
Incorrect
Your Answer : A
In a leap year, there are 366 days. There will be 52 complete weeks (52*7=364 days) and 2 days are left. So, in a cycle, 1st and 2nd day of that year will repeat as 365th and 366th days of that year.
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Question 3 of 5
3. Question
Anil and Bharati entered into partnership with Rs.700 and Rs.600 respectively. After 3 months Anil withdrew 2/7 0f his stock but 3 months later, he puts back 3/5 of what he had withdrawn. The profit at the end of the year is rs.726. How much of this should Anil receive?
Correct
Answer : B
Anil’s investment for first 3 months = Rs.700 Anil’s investment for next 3 months = 700 – (2/7) of 700 = 700 – 200 = Rs.500 Anil’s investment for last 6 months = 500 + (3/5) of withdrawn amount = 500 + (3/5) of (2/7) of 700 = 500 + 120 = Rs.620 The ratio of shares in the profit of Anil and Bharati = {(700 × 3) + (500 × 3) + (620×6)} : 600 × 12 = {2100 + 1500 + 3720} : {7200} = 7320 : 7200 = 61:60 The share of Anil = (61/121) of Rs.726 = Rs.366
Incorrect
Answer : B
Anil’s investment for first 3 months = Rs.700 Anil’s investment for next 3 months = 700 – (2/7) of 700 = 700 – 200 = Rs.500 Anil’s investment for last 6 months = 500 + (3/5) of withdrawn amount = 500 + (3/5) of (2/7) of 700 = 500 + 120 = Rs.620 The ratio of shares in the profit of Anil and Bharati = {(700 × 3) + (500 × 3) + (620×6)} : 600 × 12 = {2100 + 1500 + 3720} : {7200} = 7320 : 7200 = 61:60 The share of Anil = (61/121) of Rs.726 = Rs.366
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Question 4 of 5
4. Question
There are eight friends P, Q, R, S, T, U, V and W who invested in some business in the ratio 1:2:3:4:5:6:7:8 and the duration for which they invested the money is in the ratio 8:7:6:5:4:3:2:1 respectively. Who will get the maximum profit at the end of the year?
Correct
Your Answer : C
The share in the profit will be proportional to the product of investment and the time duration. Therefore, the ratio of shares in the profit of P, Q, R, S, T, U, V and W = 1×8 : 2×7 : 3×6 : 4×5 : 5×4 : 6×3 : 7×2 : 8×1 = 8 : 14 : 18 : 20 : 20 : 18 : 14 : 8 So, both S and T will get the maximum share.
Incorrect
Your Answer : C
The share in the profit will be proportional to the product of investment and the time duration. Therefore, the ratio of shares in the profit of P, Q, R, S, T, U, V and W = 1×8 : 2×7 : 3×6 : 4×5 : 5×4 : 6×3 : 7×2 : 8×1 = 8 : 14 : 18 : 20 : 20 : 18 : 14 : 8 So, both S and T will get the maximum share.
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Question 5 of 5
5. Question
A sum of Rs.8400 was taken as a loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum, compounded annually, then the value of each instalment is:
Correct
Your Answer – C
Let the instalment be Rs.’x’ Liability at the end of the first year = 8400 + 10% of 8400 = 8400 + 840 = Rs.9240 Principle for the beginning of second year = Rs.(9240 – x) Liability at the end of second year = (9240-x) + 10% of (9240-x) = 1.1(9240-x) But, liability at the end of second year = instalment 1.1(9240-x) = x 10164 – 1.1x = x 2.1x = 10164 x = 10164/2.1 = Rs.4840 Therefore, the value of each instalment = Rs.4840
Incorrect
Your Answer – C
Let the instalment be Rs.’x’ Liability at the end of the first year = 8400 + 10% of 8400 = 8400 + 840 = Rs.9240 Principle for the beginning of second year = Rs.(9240 – x) Liability at the end of second year = (9240-x) + 10% of (9240-x) = 1.1(9240-x) But, liability at the end of second year = instalment 1.1(9240-x) = x 10164 – 1.1x = x 2.1x = 10164 x = 10164/2.1 = Rs.4840 Therefore, the value of each instalment = Rs.4840
