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In this series of quizzes,we will be providing most important questions on Arithmetic (Percentage, Profit Loss,TSD,Time and Work,etc) which are usually asked in the exams.In Prelims Examination,usually 10-15 questions are asked from this topic.
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Question 1 of 10
1. Question
A, B and C invested Rs.21000, Rs.12000 and Rs.15000 respectively in a business. A added Rs.1000 after every quarter and B withdrew the same after every quarter and C adds Rs.5000 after 6 months. At the end of one year,find by how much percent the profit share of B is more/less than that of A and C taken together.
Correct
Ratio of profit share of A, B and C after one year
=> (21000*3 + 22000*3 + 23000*3 + 24000*3) : (12000*3 + 11000*3 + 10000*3+ 9000*3) : (15000*6 + 20000*6)
=> 270: 126: 210
=> 45: 21: 35
Required percent = {(35+45) – 21}/(35+45) * 100 = 5900/80 = 73.75% less
Incorrect
Question 2 of 10
2. Question
The average of 9 numbers is 11. If each of these 9 numbers is multiplied by 5 and then 5 is added to each of these resultant numbers, what is the new average?
Correct
Since the average of 9 numbers is 11, total sum of all 9 numbers = 9 *11 = 99
If 5 is multiplied with each number, the effect will be same as multiplying 5 with 99.
∴ The new total after multiplying each number by 5 is 99 * 5 = 495
Now 5 is added to each number, so in total 45 is added.
∴ The new total after addition of 5 to each number = 495 + 45 = 540
∴ The new average = 540/9 = 60
Incorrect
Since the average of 9 numbers is 11, total sum of all 9 numbers = 9 *11 = 99
If 5 is multiplied with each number, the effect will be same as multiplying 5 with 99.
∴ The new total after multiplying each number by 5 is 99 * 5 = 495
Now 5 is added to each number, so in total 45 is added.
∴ The new total after addition of 5 to each number = 495 + 45 = 540
∴ The new average = 540/9 = 60
Question 3 of 10
3. Question
20 lakh tourists came to visit Jim Corbett National park in 2015. There was an increase of seven percent in the number of tourist arrivals in 2016. If the rate is further appreciated by 2 percent points in 2017, how many tourists visit the National park in year 2017?
Correct
No. of tourists to visit the National Park in 2015 = 20, 00,000
The tourists increase by 7 percent in 2016
Thus, No. of tourists in 2016 = 1.07 X 20, 00,000 = 21, 40,000
The rate of increase is further increased by two percent points i.e. 9 percent
Thus, No. of tourists in 2017 = 1.09 X 21, 40,000 = 23, 32,600
Incorrect
No. of tourists to visit the National Park in 2015 = 20, 00,000
The tourists increase by 7 percent in 2016
Thus, No. of tourists in 2016 = 1.07 X 20, 00,000 = 21, 40,000
The rate of increase is further increased by two percent points i.e. 9 percent
Thus, No. of tourists in 2017 = 1.09 X 21, 40,000 = 23, 32,600
Question 4 of 10
4. Question
A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs.100, there would have a profit of 6%. What was the cost price of the article?
Correct
Let CP = x
106% * (x) – 80% * (x) = 100
26% * (x) = 100
x = 10000/26
x = 384.61
Incorrect
Let CP = x
106% * (x) – 80% * (x) = 100
26% * (x) = 100
x = 10000/26
x = 384.61
Question 5 of 10
5. Question
Gopal, Rana and Swami are three friends who are working in different companies. They are able to save 20%, 40% and 60% of their salaries respectively. If the ratio of their expenditure is 5 : 3 : 9 respectively, then what is the ratio of their respective salaries?
Correct
Let the salaries of Gopal, Rana and Swami be Rs G, Rs R and Rs S respectively.
They are able to save 20%, 40% and 60% of their salaries hence their expenditure will be 80%, 60% and 40% of their salaries.
Therefore, 0.8G : 0.6R : 0.4S = 5 : 3 : 9 .. (1)
From (1) we will get; 0.8G : 0.6R = 5 : 3
=> 0.8G/0.6R=5/3
=> G : R = 5 : 4 .. (i)
Also; 0.6R : 0.4S = 3 : 9
=> 0.6R/0.4S=3/9
=> R : S = 2 : 9 .. (ii)
From (i) and (ii) we will get; G : R : S = 5 : 4 : 18
Hence the required ratio is 5 : 4 : 18.
Incorrect
Let the salaries of Gopal, Rana and Swami be Rs G, Rs R and Rs S respectively.
They are able to save 20%, 40% and 60% of their salaries hence their expenditure will be 80%, 60% and 40% of their salaries.
Therefore, 0.8G : 0.6R : 0.4S = 5 : 3 : 9 .. (1)
From (1) we will get; 0.8G : 0.6R = 5 : 3
=> 0.8G/0.6R=5/3
=> G : R = 5 : 4 .. (i)
Also; 0.6R : 0.4S = 3 : 9
=> 0.6R/0.4S=3/9
=> R : S = 2 : 9 .. (ii)
From (i) and (ii) we will get; G : R : S = 5 : 4 : 18
Hence the required ratio is 5 : 4 : 18.
Question 6 of 10
6. Question
Prem had borrowed some amount from Bharat on simple interest of 20% per annum. After 3 years, he returned the loan and interest by paying 2,40,000. How much interest did Prem pay to Bharat?
Correct
Let the amount borrowed by Prem be P.
(P*20*3)/100 = 240000 – P
3P/5 + P = 240000
8P/5 = 240000
P = 150000
Interest paid by Prem to Bharat = 240000 – 150000 = 90000
Incorrect
Let the amount borrowed by Prem be P.
(P*20*3)/100 = 240000 – P
3P/5 + P = 240000
8P/5 = 240000
P = 150000
Interest paid by Prem to Bharat = 240000 – 150000 = 90000
Question 7 of 10
7. Question
Gautam travelled from his home to office at the rate of 30 kmph and comes back home at 24 kmph. If he covers the whole journey in 1 hour 48 minutes, what is the total distance travelled by him?
Correct
Let the distance between his office and home be D.
D/30 + D/24 = 1 + 48/60 = 9/5
54D/(30*24) = 9/5
D = 24 km
Total distance he travelled = 2D = 48 km
Incorrect
Let the distance between his office and home be D.
D/30 + D/24 = 1 + 48/60 = 9/5
54D/(30*24) = 9/5
D = 24 km
Total distance he travelled = 2D = 48 km
Question 8 of 10
8. Question
8 girls and 12 boys can complete a work in 4 days. If one boy alone completes the work in 60 days, then in how many days a girl will be able to finish the same work alone?
Correct
Work done by 1 boy in 1 day = 1/60
Work done by 12 boys in 1 day = 12/60 = 1/5
Work done by 12 boys in 4 days = 4/5
In 4 days they will complete 4/5 of work, so 8 girls will finish 1/5 of work in 4 days.
So 1 girl will finish 1/40 of work in 4 days.
Therefore, a girl alone will finish the work in 160 days.
Incorrect
Work done by 1 boy in 1 day = 1/60
Work done by 12 boys in 1 day = 12/60 = 1/5
Work done by 12 boys in 4 days = 4/5
In 4 days they will complete 4/5 of work, so 8 girls will finish 1/5 of work in 4 days.
So 1 girl will finish 1/40 of work in 4 days.
Therefore, a girl alone will finish the work in 160 days.
Question 9 of 10
9. Question
In three mixtures, water and spirit is in the ratio of 2: 3, 1: 3 and 2: 5 respectively. If all three mixtures are mixed in the ratio of 1: 3: 2 respectively, then what will be the ratio of water and spirit in the resulting mixture?
Correct
Let the volume of three mixtures be n, 3n and 2n liter respectively.
Hence volume of water in the resulting mixture = (n X 2/5 + 3n X 1/4 + 2n X 2/7)
= 2n/5 + 3n/4 + 4n/7 = 241n/140
Volume of spirit in the resulting mixture = (n X 3/5 + 3n X 3/4 + 2n X 5/7)
= 3n/5 + 9n/4 + 10n/7 = 599n/140
Therefore, required ratio = 241n/140 ∶ 599n/140 = 241 ∶ 599
Incorrect
Let the volume of three mixtures be n, 3n and 2n liter respectively.
Hence volume of water in the resulting mixture = (n X 2/5 + 3n X 1/4 + 2n X 2/7)
= 2n/5 + 3n/4 + 4n/7 = 241n/140
Volume of spirit in the resulting mixture = (n X 3/5 + 3n X 3/4 + 2n X 5/7)
= 3n/5 + 9n/4 + 10n/7 = 599n/140
Therefore, required ratio = 241n/140 ∶ 599n/140 = 241 ∶ 599
Question 10 of 10
10. Question
A, B and C each invested Rs.10000 to start a firm and after 1 year, their father gave them certain sum in ratio 2:5:3 which they added to their investments for the second year. The profit at the end of 2 years is distributed among A, B and C in ratio 4:7:5. Find the sum of money father distributed.
Correct
Let the sum father distributed be ’10P’
Amount added after a year by,
A = 2P
B = 5P
C = 3P
Ratio of profits at the end of 2 years = {10000*1 + (10000 + 2P)*1}: {10000*1 + (10000 + 5P)*1}: {10000*1 + (10000 + 3P)*1}
4: 7: 5 = (20000 + 2P): (20000 + 5P): (20000 + 3P)
7*(20000+2P) = 4*(20000+5P)
60000 = 6P
P = 10000
Also,
5*(20000+5P) = 7*(20000+3P)
P = 10000
Hence, we get P = 10000
Sum distributed by father = 10P = Rs.100000
Incorrect
Let the sum father distributed be ’10P’
Amount added after a year by,
A = 2P
B = 5P
C = 3P
Ratio of profits at the end of 2 years = {10000*1 + (10000 + 2P)*1}: {10000*1 + (10000 + 5P)*1}: {10000*1 + (10000 + 3P)*1}
4: 7: 5 = (20000 + 2P): (20000 + 5P): (20000 + 3P)
7*(20000+2P) = 4*(20000+5P)
60000 = 6P
P = 10000
Also,
5*(20000+5P) = 7*(20000+3P)
P = 10000
Hence, we get P = 10000
Sum distributed by father = 10P = Rs.100000