**Find solutions for all the questions at the end of each set:**

### Set A

1.A cylindrical tank 7 m in diameter, contains water to depth of 4 m. What is the total area of wetted surface?

(a) 110.5 sq.m

(a) 126.5 sq.m

(a) 131.5 sq.m

(a) 136.5 sq.m

2.The inner and outer radii of a 7 m long hollow iron right circular cylindrical pipe are 2 cm and 4 cm respectively. If 1000 cm^3 of iron weights 5 kg, what is the weight of the pipe?

(a) 264 kg

(b) 132 kg

(c) 396 kg

(d) None of these

3.A sphere is cut into two equal halves and both the halves are painted from all the sides. The radius of the sphere is r unit and the rate of painting is Rs. 8 per sq unit. What is the total cost of painting the two halves of the sphere in rupees?

(a) 6 πr^2

(b) 32 πr^2

(c) 48 πr^2

(d) Insufficient data to answer

4.Shyam bought 2 articles for Rs. 5.50/- each, and 3 articles for Rs. 3.50/- each and 3 articles for Rs. 5.50/- each and 5 articles for Rs. 1.50/- each. The average price for one article is:

(a) Rs. 3/-

(b) Rs. 3. 10/-

(c) Rs. 3. 50/-

(d) Rs. 2/-

5.Four runners started running simultaneously from a point on a circular track. They took 200 sec, 300 sec, 360 sec and 450 sec to complete one round. After how much time do they meet at the starting point for the first time?

(a) 1800 seconds

(b) 3600 seconds

(c) 2400 seconds

(d) 4800 seconds

6.Water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long, 44 m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is

(a) 2

(b) 1 ½

(c) 3

(d) 2 ½

7.The ratio of the quantities of an acid and water in a mixture is 1 : 3. If 5 litres of acid is further added to the mixture, the new ration becomes 1 : 2. The quantity of new mixture in litres is:

(a) 32

(b) 40

(c) 42

(d) 45

8.The cost of an apple is twice that of a banana and the cost of a banana is 25% loss than that of a guava. If the cost of each type of fruit increase by 10%, then the percentage increase in cost of 4 banana, 2 apples and 3 guavas is

(a) 10%

(b) 12%

(c) 16%

(d) 18%

9.If I walk at 5 km/hour, I miss a train by 7 minutes. If, however, I walk at 6 km/hour, I reach the station 5 minutes before the departure of the train. The distance (in km) between my house and the station is

(a) 6

(b) 5

(c) 4

(d) 3

10.The average age of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players. The average age of the new players is

(a) 19 years 1 month

(b) 19 years 6 month

(c) 19 years 11 month

(d) 19 years 5 month

**ANSWERS AND SOLUTION :**

1.(b) ; Required surface area = πr^2+ 2πrh

= πr(r+2h)

= 22/7 * 7/2 (7/2 + 2 * 4)

= 11* (7 + 16)/2 = 11 * 23/2

= 126.5 sq.mt

2.(b) ; Required weight of pipe = π(R^2 – r^2)h

= 22/7 (4^2 – 2^2) 700

= 26400 cm^2

= 26400 * 5/1000 kg

132 kg

3.(c) Total surface area of two halves = 3πr^2 + 3πr^2

= 6πr^2

Required cost = 8 * 6πr^2 = Rs. 48πr^2

4.(c) Required average price

= (2 × 5.5 + 3 × 3.5 + 3 × 5.5 + 5 × 1.5)/((2+3+3+5))

= (11.0 + 10.5 + 16.5 + 7.5)/13

= 45.5/13

= Rs. 3.50/-

5.(a) Required time = L.C.M of (200, 300, 360 and 450) second

= 1800 seconds

6.(a); Quantity of water flows in 1 hour = πr^2h

= (22 ×7 ×7 ×5000)/(7 ×100 ×100) = 77 cm^3

Volume of water in pipe = (50 ×44 ×7)/100 154 cm^3

so Required time = 154/77 = 2 hours

7.(d) ; Let quantity of acid in mixture = x

And quantity of water in mixture = 3x

According to question,

x + 5/3x = 1/2

=> 3x = 2x + 10

=> x = 10 litres

So, Total quantity of new mixture

= x +3x + 5 = 4x + 5

= 4 * 10 + 5 = 45 litres

8.(a); Let price of a banana be = Rs. 100/-

then, price of an apple and a guava respectively will be Rs. 200/- and Rs. 250/-

Sum of prices of 4 bananas, 2 apples and 3 guavas

= 400 + 400 + 750

= Rs. 1550/-

Sum of prices of 4 bananas, 2 apples and 3 guavas

= 110/100 * 400 * 110/100 * 400 + 110/100 * 750

= 440 + 440 + 825 = Rs. 1705/-

So, increased percentage = (1705 – 1550)/1550 * 100

= 155/1550 * 100 = 10%

9.(a) Let distance between house and station be x km

According to question

x/5 – x/6 = (7+5)/60

(6x – 5x)/30 = 12/60

7x = (30* 12)/60 = 6 km

10.(c) Total increment in age = 11 * 2 = 22 months

so Total ages of two new players

= (18 + 20) years + 22 months

= 38 years + 22 months

###

Set B

1.The average age of four boys. five years ago was 9 years. On including a new boy, the present average age of all the ﬁve is 15 years. The present age of the new boy is

(1) 14 years

(2) 6 years

(3) 15 years

(4) 19 years

2.The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 5,184 value is cut into 3 pieces whose weights are in the ratio l : 2 : 3. Find the loss involved in the cutting.

(1) Rs. 3,068

(2) Rs. 3,088

(3) Rs. 3.175

(4) Rs. 3,168

3.A discount of 30% on the marked price of a toy reduces its selling price by Rs. 30. What is the new selling price (in Rs.)?

(1) 70

(2) 21

(3) 130

(4) 100

4.Pipe A alone can ﬁll a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank in

(1) 6 hours

(2) 3.5 hours

(3) 4 hours

(4) 2 .5 hours

5.The population of a town is 15000. If the number of males increases by 8% and that of females by 10%, then the population would increase to 16300. Find the number of females in the town.

(1) 4000

(2) 6000

(3) 3000

(4) 5000

6.If Rs. 5,000 becomes Rs. 5,700 in a year's time, what will Rs. 7,000 become at the end of 5 years at the same rate of simple interest?

(1) Rs.10, 500

(2) Rs. l1, 900

(3) Rs. 12, 700

(4) Rs. 7,700

7.A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. The distance (in metres) between them after 6 minutes is

(1) 190

(2) 200

(3) 100

(4) 150

8.‘A’ sells an article to ‘B’ at a profit of 20% and ‘B’ sells it to ‘C’ at a profit of 25%. If ‘C’ pays Rs.1200,the cost price of the article originally (in Rs.) is

(1) 700

(2) 600

(3) 1,000

(4) 800

9.The least number which when divided by 35,45, 55 leaves the remainder 18,28,38 respectively is

(1) 3448

(2)3482

(3) 2468

(4) 3265

10.A farmer divides his herd of n cows among his four sons, so that the first son gets one-half the herd, the second one- fourth, the third son 1/5 and the fourth son 7 cows. Then the value of n is

(1) 240

(2) 100

(3) 180

(4) 140

**ANSWERS AND SOLUTION :**

1.(4) Sum of the present ages of four boys

= 9 * 4 + 20 = 56 years

Sum of the present ages of five boys

= 15 * 5 = 75 years

so Present age of new boy

= 75 – 56 = 19 years

2.(4) If the weight of a piece of diamond be 6 x units, then Original price α(6x)^2 = 36kx^2

so 36.kx^2 = 5184 ………(i)

Again,

New price = k(x^2 + 4x^2 + 9x^2)

= 14kx^2

= (14 * 5184)/36 = Rs. 2016

so Loss = 5184 – 2016

= Rs. 3168

3.(1) 30% = Rs. 30

so 100% = Rs. 100

New S.P. = 100 -30 = Rs. 70

4.(4) Part of the tank filled by both pipes in two hours

= 2 (1/8 + 1/6) = 2(3 + 4)/24 = 7/12

Remaining part = 1 – 7/12 = 5/12

Time taken by B in filling the remaining part

= 5/12 * 6 = 5/2 = 2 1/2 hours

5.(4) If the number of females be x, then number of males = 15000 – x

so x * 10/100 + (15000 –x) * 8/100

= 16300 – 15000

= 10x + 120000 – 8x

= 1300 * 100

=> 2x = 130000 – 120000 = 10000

=>x = 5000

6.(2) Interest = 5700 – 5000

= Rs. 700

so Rate = (700 * 100)/(5000 * 1) = 14%

Case II,

Interest = Principal * Time * Rate/100

= (7000 * 5 * 14)/100 = Rs. 4900

Amount = 7000 + 4900

= Rs. 11900

7.(3) Relative speed = 11 – 10 = 1 kmph

Distance covered in 6 minutes

= 1000/60 * 6 metre = 100 metre

so Remaining distance =200-100=100

8.(4) Effective profit percent

= (20 + 25 + (20 * 25)/100) = 50%

so Original cost price = 100/150 * 1200 = Rs.800

9.(1)

10.(4) According to the question.

n/2 + n/4 + n/5 + 7 = n

=> (10n + 5n + 4n)/20 + 7 = n

=> 19n/20 + 7 = n

=> n – 19n/20 = 7

=> n/20 = 7

=> n = 20 * 7 = 140

## No comments:

## Post a Comment