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1. In a cricket team of 11 players, one player weighing 72 kg got injured and was replaced by a new player thereby increasing the average weight of the entire team by 100 gm. What is the weight of the new player?

2. The area of a circular field is 9856 cm^{2}. If a person crosses the field along the diameter, calculate the distance that he will travel (in cm)

3. If P, Q and R started a business by initial investments of Rs.10000, Rs.15000 and Rs.20000 respectively and after 6 months P, Q and R additionally invested Rs.10000, Rs.8000 and Rs.6000 respectively, then what is the share of Q in the profit of Rs.144000 after 1 year?

4. An election was contested by two parties A and B. A got 18 percentage points more votes in comparison to B and B got 82000 votes. Find by what margin did A win the election?

5. A watch was sold at a loss of 15%. Had it been sold for Rs.300 more, the seller would have gained 15% instead. What is the no-profit, no-loss selling price of the watch?

6. There are two mixtures of milk and water A and B respectively. The ratio of milk and water in these two mixtures is 7 : 12 and 2 : 5 respectively. If both the mixtures are mixed in a way such that the ratio of water to milk in resulting mixture is 7 : 3 then find out the ratio in which first mixture A is mixed with the second mixture B?

7. Ratio of population of Banglore to Chennai is 5 : 9 and the ratio of number of males in Banglore and Chennai is 7 : 15. What is the ratio of number of females in Chennai to number of females in Banglore?

8. A sum of Rs. 2000 is lent in two parts on simple interest, one at 8% per annum and other at 9.2% per annum for 7 years and the interest obtained is Rs. 1204. What are the two parts respectively?

9. A man going to his office at a speed of 40 kmph, he reaches the office 15 minutes late and while going at a speed of 56 kmph, he reaches the office late by five minutes. At what speed should the man travel to reach the office on time?

10. One pipe A can fill the tank completely in 24 minutes and another pipe B can fill it completely in 30 minutes. A 3^{rd} pipe which is drain pipe empties the tank completely in 12 minutes. The inlet pipes are opened for 10 minutes and then drain pipe is also opened. Find the time taken to empty the water tank.

**Check your Answers below:**

##### 1. Question

In a cricket team of 11 players, one player weighing 72 kg got injured and was replaced by a new player thereby increasing the average weight of the entire team by 100 gm. What is the weight of the new player?

Ans:4

Let the original weight of the new player is W kg and the average weight of the original 11 players is n kg.

Hence total weight of the 11 players = 11n kg

Now according to the question, (11n-72 + W)/11=n+0.1

=> 11n – 72 + W = 11n + 1.1

=> W = 72 + 1.1

=> W = 73.1 kg##### 2. Question

The area of a circular field is 9856 cm

^{2}. If a person crosses the field along the diameter, calculate the distance that he will travel (in cm)Ans:2

πr^{2}= 9856=> (22/7) r^{2}=9856=> r

^{2}=9856*7/22=> r= 56

=> So, the distance that he has to travel = 2*56 = 112

##### 3. Question

If P, Q and R started a business by initial investments of Rs.10000, Rs.15000 and Rs.20000 respectively and after 6 months P, Q and R additionally invested Rs.10000, Rs.8000 and Rs.6000 respectively, then what is the share of Q in the profit of Rs.144000 after 1 year?

Ans:1

Investment of P = (10000 x 6) +(20000 x 6) = (30000 x6)

Investment of Q = (15000 x 6) +(23000 x 6) = (38000 x6)

Investment of R = (20000 x 6) +(26000 x 6) = (46000 x6)

Ratio of investments of P, Q and R

= (30000 x6): (38000 x6): (46000 x6)

= 30: 38: 46 = 15: 19: 23

Share of Q = (19/57) x 144000 = Rs.48000.##### 4. Question

An election was contested by two parties A and B. A got 18 percentage points more votes in comparison to B and B got 82000 votes. Find by what margin did A win the election?

Ans:5

Let the votes got by A = x%

Votes got by B = x-18%

And x+x-18% = 100%

2x = 118%

x = 59%

Votes obtained by A = 59%

Votes obtained by B = 59-18 = 41%

41/100x = 82000

x = 200000 votes

Margin = 18% of total votes

= 18*200000/100

= 36000 votes##### 5. Question

A watch was sold at a loss of 15%. Had it been sold for Rs.300 more, the seller would have gained 15% instead. What is the no-profit, no-loss selling price of the watch?

Ans:2

Initial price = x

15% loss price = 85x/100

According to question, (85x/100)+300 = x (1+15/100)= 115x/100

→ 300 = (115x/100)-(85x/100)

→ 300 = 30x/100

→ x = 300*100/30=1000

Hence the correct answer is option B.##### 6. Question

There are two mixtures of milk and water A and B respectively. The ratio of milk and water in these two mixtures is 7 : 12 and 2 : 5 respectively. If both the mixtures are mixed in a way such that the ratio of water to milk in resulting mixture is 7 : 3 then find out the ratio in which first mixture A is mixed with the second mixture B?

Ans:3

Let’s suppose m kg of mixture A is mixed with n kg of mixture B.Hence the total volume of the milk in resulting mixture = (7m/19+2n/7) literTotal volume of the resulting mixture = (m + n) liter

According to the question,

=> 10 (7m/19+2n/7) = 3m + 3n

By solving the above equation we will get,

=> m/n=19/91

##### 7. Question

Ratio of population of Banglore to Chennai is 5 : 9 and the ratio of number of males in Banglore and Chennai is 7 : 15. What is the ratio of number of females in Chennai to number of females in Banglore?

Ans:5

let the population of Banglore be 5n.

According to the question; “Ratio of population of Banglore to Chennai is 5 : 9” hence population of Chennai will be 9n.

Also according to the question; Number of males in Banglore = 7m

Number of males in Chennai = 15m

As we know that;

Total population = Number of Male + Number of females

Let number of females in Banglore and Chennai be p and q respectively.

Therefore; 5/9 = (7m+p)/(5m+q)

From this equation we can’t determine the ratio of p : q.##### 8. Question

A sum of Rs. 2000 is lent in two parts on simple interest, one at 8% per annum and other at 9.2% per annum for 7 years and the interest obtained is Rs. 1204. What are the two parts respectively?

Ans:1

Let the two parts lent be x and (2000-x)

Simple interest = 1204 = (x*7*8)/100 + [(2000-x) *7*9.2]/100

120400 = 56x + 128800 – 64.4x

8.4x = 8400

x = 1000

So, the two parts are Rs 1000 and Rs 1000.##### 9. Question

A man going to his office at a speed of 40 kmph, he reaches the office 15 minutes late and while going at a speed of 56 kmph, he reaches the office late by five minutes. At what speed should the man travel to reach the office on time?

Ans:4

Let ‘d’ km be the distance the man travels to reach his office and ‘t’ hrs be the usual time taken to reach office on time.

Therefore d = 40(t + 1/4) = 56(t + 1/12)

t = 1/3 hr

Therefore d = 40(1/3 + 1/4)

d = 40(7/12) = 70/3 km.

Therefore usual speed of the man = distance/time = (70/3)/(1/3) = 70 kmph

Hence the correct option is (4).##### 10. Question

One pipe A can fill the tank completely in 24 minutes and another pipe B can fill it completely in 30 minutes. A 3

^{rd}pipe which is drain pipe empties the tank completely in 12 minutes. The inlet pipes are opened for 10 minutes and then drain pipe is also opened. Find the time taken to empty the water tank.Ans:3

=> Let the tank is emptied after x minutes.

Means, The third drain pipe is opened only for x minutes

=> x/12 – (x+10)/24 – (x+10)/30 = 0

=> 10x – 5(x+10) – 4 (x+10) / 120 = 0

=> 10x – 5x – 50 – 4x – 40 = 0

=> x = 90