**1. A circular garden has a circumference of 440 m. There is a 7 m wide border inside the garden along its periphery. The area of the border is :**

(1) 2918 m^2

(2) 2921 m^2

(3) 2924 m^2

(4) 2926 m^2

(5) 2950 m^2

**2. In a bag, there are three types of coins – 1 rupee, 50 paise and 25 paise in the ratio of 3 : 8 : 20. Their total value is Rs. 372. The total number of coins is**

(1) 1200

(2) 961

(3) 744

(4) 612

(5) 800

**3. Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?**

(1) 8 min

(2) 12 min

(3) 15 min

(4) 20 min

(5) 17 min

**4. A train travelling 25 km an hour leaves Delhi at 9 a.m. and another train travelling 35 km an hour starts at 2 p.m. in the same direction. How many km from Delhi will they be together?**

(1) 437 ½ km

(2) 436 ½ km

(3) 435 ½ km

(4) 434 ½ km

(5) 435 km

**5. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :**

(1) 4 days

(2) 8 days

(3) 6days

(4) 7 days

(5) 5 days

**6. A and B can do a job together in 7 days. A is 1 3/4 times as efficient as B. The same job can be done by A alone in :**

(1) 12 days

(2) 11 days

(3) 15 days

(4) 16 days

(5) 10 days

**7. A man saves Rs 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.**

(1) 661.01

(2) 662.01

(3) 663.01

(4) 664.01

(5) None of these

**8. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq.ft, how many feet of fencing will be required?**

(1) 90 feet

(2) 85 feet

(3) 88 feet

(4) 84 feet

(5) 82 feet

**9. The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum reckoned half – yearly is :**

(1) Rs. 2

(2) Rs. 3

(3) Rs. 4

(4) Rs. 5

(5) None of these

**10. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.**

(1) 5 : 2

(2) 5 : 2

(3) 4 : 25

(4) 5 : 4

(5) 2 : 6

**11. A starts business with Rs. 3500 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**

(1) 1000

(2) 10000

(3) 12000

(4) 5000

(5) 9000

1. (4) : 2πR = 440

2 × 22/7 x R = 440

R = 70 m.

Inside radius = ( 70 – 7 ) m = 63 m

Area of the border = π [(70)^2 – (63)^2]m^2

= [22/7 x (70 + 63 ) x ( 70 – 63 ) ] m2 = 2926m^2

2. (2)

3. (1) : let B be closed after x min. then ,

Part filled by (A+B) in x min. +part filled by A in (18-x)min.=1

Therefore x*((1/24)+(1/32))+(18-x)*(1/24)=1

(7x/96) + ((18-x)/24)=1.

7x +4*(18-x)=96.

Hence, be must be closed after 8 min.

4. (1) : The first train has a start of 25 / 5 km and the second train gains ( 35 – 25 ) or 10 km per hour.

The second train will gain 25 x 5 km in (25 x5) / 10 or 12 ½ hours.

The required distance from Delhi = 12 ½ x 35 km = 437 ½ km

Shortcut : (try this )

Meeting point’s distance from starting point

= (S1 x S2 x Difference in time) / Difference in speed ( S1 and S2 are the speed )

5. (2) : (A+B+C)=1/6

A's one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12

C's one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24

(A+C)'s one day work= 1/12+1/24= 1/8

so the work will be completed in 8 days

6. (2) : (A's 1 day's work) : (B's 1 day's work) = 7 /4 : 1 = 7 : 4

Let A’s and B’s 1 days’ work be 7 x and 4 x respectively

then , 7x + 4x= 1/7 11x = 1/7 x = 1/77

A’s 1 days = (1) / (77) x 7 = 1/ 11

A alone can do this job = 11 days

7. (2)

8. (3) : We are given with length and area, so we can find the breadth.

as Length x Breadth = Area

=> 20 x Breadth = 680

=> Breadth = 34 feet

Area to be fenced = 2B + L = 2 x 34 + 20

= 88 feet

9. (2) : S. I = Rs. ((1200 ×10 ×1)/100) = Rs. 120

C. I. = Rs. = Rs. 123.

Difference = Rs. 3

10. (3) : Let the diagonals of the squares be 2x and 5x.

Then ratio of their areas will be

Area of square=(1/2) x Diagonal2

(1/2 ) x 2x2 : (1/2) x 5x2

4x2 :25x2 =4:25

10. (5) : Let B contribution is x.

(3500 x 12) /7x=2/3 =>14x=126000=>x=Rs9000

1. (4) : 2πR = 440

2 × 22/7 x R = 440

R = 70 m.

Inside radius = ( 70 – 7 ) m = 63 m

Area of the border = π [(70)^2 – (63)^2]m^2

= [22/7 x (70 + 63 ) x ( 70 – 63 ) ] m2 = 2926m^2

2. (2)

3. (1) : let B be closed after x min. then ,

Part filled by (A+B) in x min. +part filled by A in (18-x)min.=1

Therefore x*((1/24)+(1/32))+(18-x)*(1/24)=1

(7x/96) + ((18-x)/24)=1.

7x +4*(18-x)=96.

Hence, be must be closed after 8 min.

4. (1) : The first train has a start of 25 / 5 km and the second train gains ( 35 – 25 ) or 10 km per hour.

The second train will gain 25 x 5 km in (25 x5) / 10 or 12 ½ hours.

The required distance from Delhi = 12 ½ x 35 km = 437 ½ km

Shortcut : (try this )

Meeting point’s distance from starting point

= (S1 x S2 x Difference in time) / Difference in speed ( S1 and S2 are the speed )

5. (2) : (A+B+C)=1/6

A's one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12

C's one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24

(A+C)'s one day work= 1/12+1/24= 1/8

so the work will be completed in 8 days

6. (2) : (A's 1 day's work) : (B's 1 day's work) = 7 /4 : 1 = 7 : 4

Let A’s and B’s 1 days’ work be 7 x and 4 x respectively

then , 7x + 4x= 1/7 11x = 1/7 x = 1/77

A’s 1 days = (1) / (77) x 7 = 1/ 11

A alone can do this job = 11 days

7. (2)

8. (3) : We are given with length and area, so we can find the breadth.

as Length x Breadth = Area

=> 20 x Breadth = 680

=> Breadth = 34 feet

Area to be fenced = 2B + L = 2 x 34 + 20

= 88 feet

9. (2) : S. I = Rs. ((1200 ×10 ×1)/100) = Rs. 120

C. I. = Rs. = Rs. 123.

Difference = Rs. 3

10. (3) : Let the diagonals of the squares be 2x and 5x.

Then ratio of their areas will be

Area of square=(1/2) x Diagonal2

(1/2 ) x 2x2 : (1/2) x 5x2

4x2 :25x2 =4:25

10. (5) : Let B contribution is x.

(3500 x 12) /7x=2/3 =>14x=126000=>x=Rs9000

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