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

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

### Set A

### 1.The average of 7 numbers is 8. If one number is added, their average is 9. Then the added number is

(1) 12

(2) 11

(3) 16

(4) 14

2.With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. The total journey is

(1) 35 km

(2) 60 km

(3) 70 km

(4) 50 km

3.Three students A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 2. B’s runs to C’s runs are also in the same ratio. Together they score 342 runs. Then the runs scored by B are

(1) 216

(2) 108

(3) 90

(4) 171

4.A trader ﬁxes selling prices of commodities after increasing them by 10% and offers 10%

rebate on selling prices. The per cent. gain or loss is

(1) 1% gain

(2) 0.9% gain

(3) 1.2% loss

(4) 1% loss

5.B borrowed Rs. 5,000 from A at 6% p. a. simple interest and lends it to C at compound interest of 10% p. a. If B collects the money back from C after 2 years and repays A, the proﬁt made by B in the transaction is

(1) Rs. 600

(2) Rs. 1,050

(3) Rs. 500

(4) Rs. 450

6.Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 Km from one of the stations. The ratio of their speeds is

(1) 11 :20

(2) 20 :9

(3) 9:20

(4) 11:9

7.The least number which is divisible by all the natural numbers upto and including 10 is

(1) 7560

(2) 1260

(3) 5040

(4) 2520

8.40 men can finish a work in 15 days. If the work is to be completed 3 days earlier, how many more people should be employed?

(1) 8

(2) 10

(3) 15

(4) 10

9.A father is 7 years older than the mother and the mother’s age now is 3 times the age of the daughter. The daughter is 10 years old now. What was the father’s age when the daughter was born?

(1) 27 years

(2) 37 years

(3) 15 years

(4) 40 years

10.Of the three numbers, the first is twice the second and is half of the third. If the average of these numbers is 56, the numbers in order are.

(1) 96, 24, 48

(2) 96, 48, 24

(3) 48, 96, 24

(4) 48, 24, 96

ANSWERS AND SOLUTION

1.(3) the added number

= 9 * 8 – 8 * 7

= 72 – 56 = 16

2.(3) If the required distance be x km, then,

x/35 – x/40 = 15/60

= (8x – 7x)/280 = 1/4

= x/280 = 1/4

=> x = 280/4 = 70 km

3.(2) A : B = 3 : 2 = 9 : 6

B : C = 3 : 2 = 6 : 4

so A : B : C = 9 : 6 : 4

so Runs scored by B = 6/19 * 342

= 108

4.(4) Resultant effect

= (10 – 10 – (10x10)/100)%

= -1%

Negative sings shows loss.

5.(4)

S. I = Principal * Time * Rate / 100

= (5000 * 2 * 6) / 100 = Rs. 600.

C.I = P {(1 + R/100)^t -1 }

= 5000 {(1 + 10/100)^2 -1 }

= 500 (121/100 -1)

= 5000 * 21/ 100

= Rs. 1050

B’s profit = 1050 – 600

= Rs. 450

6.(4) Time is equal

so 110/x = 90/y

=> x/y = 110/90 = 11/9

7.(4) LCM of whole numbers from 1 to 10.

= LCM of 6, 7, 8, 9 and 10

= 2520

8.(4) M1 D1 = M2 D2

=> 40 * 15 = M2 * 12

=> M2 = (40 * 15)/12 = 50

Number of additional men

=> 50 – 40 = 10

9.(1) Mother’s present age

= 30 years

Father’s present age = 37 year

Father’s age 10 years ago

= 37 – 10 = 27 years

10.(4) Second number = x (let)

First number = 2x

Third number = 4x

so x + 2x + 4x = 56 * 3

=> 7x = 56 * 3

x = 8 * 3 = 24

Other numbers are : 48 and 96

1.(3) the added number

= 9 * 8 – 8 * 7

= 72 – 56 = 16

2.(3) If the required distance be x km, then,

x/35 – x/40 = 15/60

= (8x – 7x)/280 = 1/4

= x/280 = 1/4

=> x = 280/4 = 70 km

3.(2) A : B = 3 : 2 = 9 : 6

B : C = 3 : 2 = 6 : 4

so A : B : C = 9 : 6 : 4

so Runs scored by B = 6/19 * 342

= 108

4.(4) Resultant effect

= (10 – 10 – (10x10)/100)%

= -1%

Negative sings shows loss.

5.(4)

S. I = Principal * Time * Rate / 100

= (5000 * 2 * 6) / 100 = Rs. 600.

C.I = P {(1 + R/100)^t -1 }

= 5000 {(1 + 10/100)^2 -1 }

= 500 (121/100 -1)

= 5000 * 21/ 100

= Rs. 1050

B’s profit = 1050 – 600

= Rs. 450

6.(4) Time is equal

so 110/x = 90/y

=> x/y = 110/90 = 11/9

7.(4) LCM of whole numbers from 1 to 10.

= LCM of 6, 7, 8, 9 and 10

= 2520

8.(4) M1 D1 = M2 D2

=> 40 * 15 = M2 * 12

=> M2 = (40 * 15)/12 = 50

Number of additional men

=> 50 – 40 = 10

9.(1) Mother’s present age

= 30 years

Father’s present age = 37 year

Father’s age 10 years ago

= 37 – 10 = 27 years

10.(4) Second number = x (let)

First number = 2x

Third number = 4x

so x + 2x + 4x = 56 * 3

=> 7x = 56 * 3

x = 8 * 3 = 24

Other numbers are : 48 and 96

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

### Set B

**1.A merchant purchases a wrist watch for Rs. 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price (in rupees) of the wrist watch is.**

(1) 500

(2) 600

(3) 750

(4) 800

**2.The simple and compound interests on a sum of money for 2 years are Rs. 8400 and Rs. 8652 respectively. The rate of interest per annum is**

(1) 6%

(2) 7.5%

(3) 9%

(4) 4.5%

**3.A can complete a piece of work in 12 days. B is 60% more efficient than A. the number of days that B will take to complete the same work is**

(1) 6

(2) 7 1/2

(3) 8

(4) 8 1/2

**4.Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all the three pipes are open, empty tank becomes full in one hour. The capacity of the tank (in gallons) is**

(1) 800

(2) 600

(3) 500

(4) 400

**5.A dealer marks his goods 30% above his cost price and then allows 15% discount on it. What is the cost price of an article on which he gains Rs. 84?**

(1) Rs. 800

(2) Rs. 560

(3) Rs. 373.33

(4) Rs. 280

**6.A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95. Then the marked price is**

(1) Rs. 100

(2) Rs. 110

(3) Rs. 120

(4) Rs. 130

**7.A and B enter into partnership with capitals in the ratio 5 : 6. At the end of 8 months A wirhdraws his capital. They received profits in the ratio 5 :9. B invested the capital for**

(1) 6 months

(2) 8 months

(3) 10 months

(4) 12 months

**8.The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and radius 3 cm, is**

(1) 640

(2) 600

(3) 500

(4) 480

**9.If A travels to his school from his house at the speed of 3 km/hr then he reaches the school 5 minutes late. If he travels at the speed of 4 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is**

(1) 1 km

(2) 2 km

(3) 3 km

(4) 4 km

**10.A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120 m behind in 18 seconds. The speed of the second train is**

(1)26 km/hr

(2) 35 km/hr

(3) 36 km/hr

(4) 63 km/hr

**ANSWERS AND SOLUTION :**

1.(2) If the marked price of the wrist watch be Rs. x, then

x * 90/100 = (450 * 120)/100 = 540

=> x = (540 * 100)/90 = Rs. 600

2.(1) Difference = Rs.(8652 – 8400)

= Rs. 252

so Rate = (2 * Difference)/S.I * 100

= (2 * (252/8400) * 100 = 6%

3.(2) Ratio of their efficiency

= 100 : 160 = 5 : 8

so Ratio of time taken = 8 : 5

so Time taken by B

= 12 * 5/8 = 15/2 = 7 1/2 days

4.(2) Capacity of the tank = x gallons.

so Part of the tank filled in 1 minute

= x/24 + x/40 – 30

so 60 (x/24 + x/40 – 30) = x

so x/24 + x/40 – x/60 = 30

=> (5x + 3x – 2x)/120 = 30

=> x/20 = 30

x = 600 gallons

5.(1)

CP of article = Rs. x

so Marked price = 130x/100 = Rs. 13x/100

so S.P.

= 13x/10 * 85/100 = Rs. 221x/200

so 221x/200 – x = 84 => 21x/200 = 84

=> x = (84 * 200)/21 = Rs. 800

6.(2) Marked price = Rs. x. then.

(x * 95)/100 = (95 * 110)/100

=> x = Rs. 110

7.(4) If b invested for y months, then

(5* 8)/(6 * y) = 5/9

=> y = 12 months

8.(1) volume of the cylinder = πr^2 h

= π × (3)^2 ×8 = 72 πcm^3

Volume of one coin

= π×(0.75)^2 ×0.2

so Number of coins

= 72π/(π ×0.75 × 0.75 ×0.2) = 640

9.(2) If the distance between the school and home be x km. then

x/3 – x/4 = 10/60

=> x/12 = 1/6

x = 1/6 * 12 = 2 km

10.(3) 60 kmph = (60 * 5)/18 m/sec

= 50/3 m/sec

If the speed of second train be x m/sec, then

50/3 – x = 120/18 = 20/3

x = 50/3 – 20/3 = 10 m/sec

= (10 * 18/5) kmph

= 36 kmph

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