1. A starts business with Rs. 35,000 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B’s contribution in the capital?

A) Rs .7500

B) Rs. 8000

C) Rs. 8500

D) Rs. 9000

Answer: D

Explanation:

Ratio in which profit is to be divided = 2 : 3

Assume that B's contribution to the capital = b

⇒ 3500 × 12 : b × 7 = 2 : 3

⇒ 3500 × 12/7 b = 2/3

⇒ b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000

2. Anand and Deepak started a business investing Rs. 22,500 and Rs.35,000 respectively. Out of a total profit of Rs.13,800, Deepak’s share is _____

A) Rs.5,400

B) Rs.7,200

C) Rs.8,400

D) Rs.9,400

Answer: A

Explanation:

Ratio of their investments = 22500 : 35000 = 9 : 14

So Deepak' s share = $\dfrac{9}{{23}}$ × 13800 = Rs.5,400

3. Narasimha, Madhu and pavan started a business by investing Rs.1,20,000, Rs.1,35,000 and Rs 1, 50,000 respectively. Find the share of Pavan, out of an annual profit of Rs.56,700.

A) Rs.16,800

B) Rs.18,900

C) Rs.21,000

D) none

Answer: C

Explanation:

Ratio of their investments = 120000 : 135000 : 150000 = 8 : 9 : 10

Share of Pavan = $\dfrac{10}{{27}}$ × 56700 = 21,000

4. Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 18,the first number is :

A) 20

B) 21

C) 23

D) 25

Answer: B

Explanation:

Let the numbers be a,b,c,d

Given, a + b + c = 48, b + c + d = 45

Now, d = 18

thus, b + c + 18 = 45 ⇒ b + c = 27

Putting the value of b + c in a + b + c = 48

a + 27 = 48 ⇒ a = 21

5. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3 . Find his average after 17th inning.

A) 39

B) 38

C) 38.5

D) 39.5

Answer: A

Explanation:

Consider the avg for first 16 innings is x.

Then total runs scored till 16 innings is 16x.

Total runs after 17 innings = 16x + 87.

Thus, $\dfrac{{16x + 87}}{{17}} = x + 3$ ⇒ x = 36

So his average after 17 innings = 39.

6. Three years ago , the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A’s present age is :

A) 30 yrs

B) 35 yrs

C) 40 yrs

D) 48 yrs

Answer: C

Explanation:

Sum of the present ages of A, B and C = (27× 3 + 3 × 3) years = 90 years.

Sum of the present ages of B and C = (20 × 2 + 5 × 2) years = 50 years.

A's present age = 90 – 50 = 40 years.

7.The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :

A) 25

B) 30

C) 35

D) 40

Answer: A

Explanation:

Let the six numbers be, a, b, c, d, e, f.

a + b + c + d + e + f = 30 × 6 = 180 - - - - (1)

a + b + c + d = 25 × 4 = 100 - - - - (2)

d + e + f = 35 × 3 = 105 - - - - (3)

Add 2nd and 3rd equations and subtract 1st equation from this.

d = 25

8. A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit . For how long B’s money was used.

A) 6 months

B) 9 months

C) 10 months

D) 1 year

Answer: C

Explanation:

B received 2/3 of the profit ⇒Their profits ratio = A : B = 1 : 2

Let the total capital = 4 units

Then A's capital = 1

B's capital = 3

Assume B's money was used for b months

Then A : B = 1 × 15 : 3 × b = 1 : 2

⇒ 15 : 3b = 1 : 2

⇒ $\dfrac{{15}}{{3b}} = \dfrac{1}{2}$

⇒ b = 10

9. At an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?

A) 672

B) 700

C) 749

D) 848

Answer: B

Explanation:

Let the total votes are 100x. Then winning candidate got 84x, and losing candidate got 16x.

⇒ 84x – 16 x = 476

⇒ 68 x = 476

⇒ x = 7

Total votes are 700.

10. A man buys a cycle for Rs.1400 and sells it at loss of 15%. What is the selling price of the cycle?

A) Rs.1090

B) Rs.1160

C) Rs.1202

D) Rs.1190

Answer: D

Explanation:

S.P = 85% of Rs.1400 ⇒ Rs.($\dfrac{85}{100}$ ×1400) = Rs.1190.

11. A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs 6.50 per kg .What will be his gain percent?

A) 4 1/6 %

B) 6 1/4 %

C) 8 1/3 %

D) 20%

Answer: C

Explanation:

Price per 1 kg = $\dfrac{420}{70}$ = Rs.6.

Profit per 1 kg = Rs.6.5 – Rs.6 = Rs.0.5

Profit for 70 kg = 0.5 × 70 = Rs.35

Gain % = $\dfrac{35}{420}$ × 100= 8.33% = 8 1/3

12. By selling 300 apples a seller gains the selling price of 60 apples. The gain percent of the seller is

A) 200

B) 20%

C) 25%

D) 16 2/3%

Answer: C

Explanation:

We know that SP − CP = Profit

⇒300SP - 300CP = 60SP

⇒240SP = 300CP

⇒ $\dfrac{{SP}}{{CP}} = \dfrac{{300}}{{240}}$ = $\dfrac{5}{4}$

Let SP = 5, and CP = 4

So profit percentage = $\dfrac{1}{4} \times 100 = 25\% $

13. The average monthly salary of 8 workers and one supervisor in a factory was $\$$430. When the supervisor, whose salary was $\$$870 per month, retired, a new person was appointed and then the average salary of 9 people was $\$$400 per month. The salary of the new supervisor is:

A. $700

B. $600

C. $430

D. $400

Answer: B

Explanation:

Total salary of 8 workers and supervisor together = 9 × 430 = 3870

Now total salary of 8 workers = 3870 − 870 = 3000

Total salary of 9 workers including the new supervisor = 9 × 400 = 3600

Salary of the new supervisor = 3600 − 3000 = 600

14. The average of the first five prime numbers greater than 20 is:

A. 32.20

B. 31.00

C. 31.01

D. 32.00

Answer: A

Explanation:

Required prime numbers are 23, 29, 31, 37, 4.

Average will be (23 + 29 + 31 + 37 + 41)/5 = 32.20

15. The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is:

A. 45

B. 34

C. 43

D. 40

E. None of these

Answer: D

Explanation:

Average score = 37

Grace mark 3 is given to 35 student then its average will be 3.

Hence new average = 37 + 3 = 40

16. The average age of a group of 10 students is 14 years. If 5 more students join the group, the average age rises by 1 year. The average age of the new students is:

A. 15 years

B. 17 years

C. 16 years

D. 18 years

E. None of these

Answer: D

Explanation:

Total age of the 10 students = 10 × 14 = 140

Total age of 15 students including the newly joined 5 students = 15 × 15 = 225

Total age of the new students = 225 − 140 = 85

Average age = 85/5 = 17 years

17. It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3 cms, How much did it rain on Wednesday?

A. 3 cms

B. 10.5 cms

C. 15 cms

D. 2.62 cms

E. 4.5 cms

Answer: B

Explanation:

Let the rainfall on wednesday = 6x.

∴ Rainfall on the remaining days = 6x

Given,

(6x + 6x )/7 = 3

⇒12x = 21

⇒6x = 10.5

A) Rs .7500

B) Rs. 8000

C) Rs. 8500

D) Rs. 9000

Answer: D

Explanation:

Ratio in which profit is to be divided = 2 : 3

Assume that B's contribution to the capital = b

⇒ 3500 × 12 : b × 7 = 2 : 3

⇒ 3500 × 12/7 b = 2/3

⇒ b = (3500 × 12 × 3)/(2 × 7) = 500 × 6 × 3 = 9000

2. Anand and Deepak started a business investing Rs. 22,500 and Rs.35,000 respectively. Out of a total profit of Rs.13,800, Deepak’s share is _____

A) Rs.5,400

B) Rs.7,200

C) Rs.8,400

D) Rs.9,400

Answer: A

Explanation:

Ratio of their investments = 22500 : 35000 = 9 : 14

So Deepak' s share = $\dfrac{9}{{23}}$ × 13800 = Rs.5,400

3. Narasimha, Madhu and pavan started a business by investing Rs.1,20,000, Rs.1,35,000 and Rs 1, 50,000 respectively. Find the share of Pavan, out of an annual profit of Rs.56,700.

A) Rs.16,800

B) Rs.18,900

C) Rs.21,000

D) none

Answer: C

Explanation:

Ratio of their investments = 120000 : 135000 : 150000 = 8 : 9 : 10

Share of Pavan = $\dfrac{10}{{27}}$ × 56700 = 21,000

4. Out of four numbers ,the average of first three is 16 and that of the last three is 15. If the last number is 18,the first number is :

A) 20

B) 21

C) 23

D) 25

Answer: B

Explanation:

Let the numbers be a,b,c,d

Given, a + b + c = 48, b + c + d = 45

Now, d = 18

thus, b + c + 18 = 45 ⇒ b + c = 27

Putting the value of b + c in a + b + c = 48

a + 27 = 48 ⇒ a = 21

5. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3 . Find his average after 17th inning.

A) 39

B) 38

C) 38.5

D) 39.5

Answer: A

Explanation:

Consider the avg for first 16 innings is x.

Then total runs scored till 16 innings is 16x.

Total runs after 17 innings = 16x + 87.

Thus, $\dfrac{{16x + 87}}{{17}} = x + 3$ ⇒ x = 36

So his average after 17 innings = 39.

6. Three years ago , the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A’s present age is :

A) 30 yrs

B) 35 yrs

C) 40 yrs

D) 48 yrs

Answer: C

Explanation:

Sum of the present ages of A, B and C = (27× 3 + 3 × 3) years = 90 years.

Sum of the present ages of B and C = (20 × 2 + 5 × 2) years = 50 years.

A's present age = 90 – 50 = 40 years.

7.The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is :

A) 25

B) 30

C) 35

D) 40

Answer: A

Explanation:

Let the six numbers be, a, b, c, d, e, f.

a + b + c + d + e + f = 30 × 6 = 180 - - - - (1)

a + b + c + d = 25 × 4 = 100 - - - - (2)

d + e + f = 35 × 3 = 105 - - - - (3)

Add 2nd and 3rd equations and subtract 1st equation from this.

d = 25

8. A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit . For how long B’s money was used.

A) 6 months

B) 9 months

C) 10 months

D) 1 year

Answer: C

Explanation:

B received 2/3 of the profit ⇒Their profits ratio = A : B = 1 : 2

Let the total capital = 4 units

Then A's capital = 1

B's capital = 3

Assume B's money was used for b months

Then A : B = 1 × 15 : 3 × b = 1 : 2

⇒ 15 : 3b = 1 : 2

⇒ $\dfrac{{15}}{{3b}} = \dfrac{1}{2}$

⇒ b = 10

9. At an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?

A) 672

B) 700

C) 749

D) 848

Answer: B

Explanation:

Let the total votes are 100x. Then winning candidate got 84x, and losing candidate got 16x.

⇒ 84x – 16 x = 476

⇒ 68 x = 476

⇒ x = 7

Total votes are 700.

10. A man buys a cycle for Rs.1400 and sells it at loss of 15%. What is the selling price of the cycle?

A) Rs.1090

B) Rs.1160

C) Rs.1202

D) Rs.1190

Answer: D

Explanation:

S.P = 85% of Rs.1400 ⇒ Rs.($\dfrac{85}{100}$ ×1400) = Rs.1190.

11. A shopkeeper purchased 70 kg of potatoes for Rs.420 and sold the whole lot at the rate of Rs 6.50 per kg .What will be his gain percent?

A) 4 1/6 %

B) 6 1/4 %

C) 8 1/3 %

D) 20%

Answer: C

Explanation:

Price per 1 kg = $\dfrac{420}{70}$ = Rs.6.

Profit per 1 kg = Rs.6.5 – Rs.6 = Rs.0.5

Profit for 70 kg = 0.5 × 70 = Rs.35

Gain % = $\dfrac{35}{420}$ × 100= 8.33% = 8 1/3

12. By selling 300 apples a seller gains the selling price of 60 apples. The gain percent of the seller is

A) 200

B) 20%

C) 25%

D) 16 2/3%

Answer: C

Explanation:

We know that SP − CP = Profit

⇒300SP - 300CP = 60SP

⇒240SP = 300CP

⇒ $\dfrac{{SP}}{{CP}} = \dfrac{{300}}{{240}}$ = $\dfrac{5}{4}$

Let SP = 5, and CP = 4

So profit percentage = $\dfrac{1}{4} \times 100 = 25\% $

13. The average monthly salary of 8 workers and one supervisor in a factory was $\$$430. When the supervisor, whose salary was $\$$870 per month, retired, a new person was appointed and then the average salary of 9 people was $\$$400 per month. The salary of the new supervisor is:

A. $700

B. $600

C. $430

D. $400

Answer: B

Explanation:

Total salary of 8 workers and supervisor together = 9 × 430 = 3870

Now total salary of 8 workers = 3870 − 870 = 3000

Total salary of 9 workers including the new supervisor = 9 × 400 = 3600

Salary of the new supervisor = 3600 − 3000 = 600

14. The average of the first five prime numbers greater than 20 is:

A. 32.20

B. 31.00

C. 31.01

D. 32.00

Answer: A

Explanation:

Required prime numbers are 23, 29, 31, 37, 4.

Average will be (23 + 29 + 31 + 37 + 41)/5 = 32.20

15. The average score of 35 students in a class is 37. If every student is given 3 grace marks, the new average of the class is:

A. 45

B. 34

C. 43

D. 40

E. None of these

Answer: D

Explanation:

Average score = 37

Grace mark 3 is given to 35 student then its average will be 3.

Hence new average = 37 + 3 = 40

16. The average age of a group of 10 students is 14 years. If 5 more students join the group, the average age rises by 1 year. The average age of the new students is:

A. 15 years

B. 17 years

C. 16 years

D. 18 years

E. None of these

Answer: D

Explanation:

Total age of the 10 students = 10 × 14 = 140

Total age of 15 students including the newly joined 5 students = 15 × 15 = 225

Total age of the new students = 225 − 140 = 85

Average age = 85/5 = 17 years

17. It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3 cms, How much did it rain on Wednesday?

A. 3 cms

B. 10.5 cms

C. 15 cms

D. 2.62 cms

E. 4.5 cms

Answer: B

Explanation:

Let the rainfall on wednesday = 6x.

∴ Rainfall on the remaining days = 6x

Given,

(6x + 6x )/7 = 3

⇒12x = 21

⇒6x = 10.5