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

### Set A

**1.The average speed of a tractor is two–fifths the average speed of a car. The car covers 450 km in 6 hours. How much distance will the tractor cover in 8 hours?**

**2.The area of a square is four times the area of a rectangle. The length of the rectangle is 25 cm and its breadth is one cm less than one–fifth of its length. What is the perimeter of the square?**

**3.What value will be obtained if the square of 22 is subtracted from the cube of 12?**

**4.The marks of six boys in a group are 48, 59, 87, 37, 78 and 57. What are the average marks of all six boys?**

**5.The ratio of the present ages of Tarun and Varun is 3 : 7. After 4 years Varun’s age will be 39 years. What was Tarun’s age 4 years ago?**

**6.The sum of five consecutive even numbers is equal to 170. What is the sum of the second largest number and the square of the smallest number amongst them together?**

**7.How many sacks are required for filling 1026 kg of rice if each sack is filled with 114 kg of rice?**

**8.Ravi consistently runs 350 metres every day except on Tuesdays when he runs 500 metres. How many kilometres will he run in two weeks? (In this question the week starts from Monday.)**

**9.The simple interest accrued in 3 years on a principal of `25,000 is three–twentieths the principal. What is the rate of simple interest pcpa?**

**10. Sumit purchased an item for Rs.6,500 and sold it at a gain of 24%. From that amount he purchased another item and sold it at a loss of 20%. What is his overall gain/loss?**

**Answers and Solution:**

Average speed of the tractor = 75 ×2/5 = 30 km/h

Distance covered by the tractor = 30 × 8 = 240 km

2.(4); Length of the rectangle = 25 cm

Breadth of the rectangle = 25/5 –1 = 4 cm

Area of the rectangle = 25 × 4 = 100 sq cm

Area of the square = 4 × 100 = 400 sq cm

Side of the square = 20 cm

Perimeter of the square = 4 × 20 = 80 cm

3.(1); (12)^3 – (22)^2 = 1728 – 484 = 1244

4.(3);

5.(4); Varun’s present age = 39 – 5 = 35 years

So, Tarun’s present age = 15 years

Tarun’s age 4 years ago = 11 years

6.(4); Let the numbers be x, x + 2, x + 4, x+6 and x + 8

According to the question,

x + x + 2 + x + 4 + x + 6 + x + 8=170

or 5x + 20 = 170

or x + 4 = 34

or x = 30.

Second largest No. = 30 + 6 = 36

Square of smallest No. = 900

Sum of these Nos. = 900 + 36 = 936

7.(4);

8.(3);

9.(1);I = 25000 ×3/20 = 3750, r = (3750*100)/75000 = 5%

10.(3); Second selling price = 6500 * 124/100 *80/100 = 6448

Loss => 6500 – 6448 = Rs. 52

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

### Set B

**1. A shopkeeper bought 80 kg of sugar at the rate of Rs.13.5 per kg. He mixed it with 120 kg of sugar costing Rs.16 per kg .In order to make a profit of 20% he must sell the mixture at**

**2. A seller gains 15% after selling an item at 10% discount on the printed price .The Ratio of the cost price and printed price of the item is**

**3. An empty tank can be filled by pipe A in 4 hours and by pipe B in 6 hours .If the two pipes are opened for 1 hour each alternately with first opening pipe A,then the tank will be filled in**

**4. Each of side of a rectangular field is diminished by 25 %,By how much percent is the area of the field diminished ?**

**5.Two numbers are 35% and 50% respectively more than a third number.The first number is what percent of the second number ?**

**6.If A : B = 3 : 4 and B : C = 8 : 9, then the ratio A : B : c is.**

**7. If a : b = b : c, then the ratio a^4 : b^4 is equal to**

**8. The numbers 11284 and 7655, when divided by a certain 3-digits number,give equal remainders. The 3-digit number is**

**9. Two numbers are in the ratio 5:6.If their LCM is 120 ,their HCF will be**

**10. A bag contains Rs. 145 in the form of one-rupee,50-paise and 25 paise coins in the ratio 3:5:7.The number of one-rupee coins is.**

**Answers and Solution:**

1.(1)

2.(1)

3.(3) Part of the tank filled in first 2 hours.

1/4 + 1/6 = (3+2)/12 = 5/12 parts

so Part of the tank filled in first 4 hours

= (2*5)/12 parts = 5/6 parts

Remaining part = 1 – 5/6 = 1/6

Now it is the turn of pipe A

Time taken to fill 1/4 part = 1 hour

So Time taken to fill 1/6 part

= 1/6*4 = 2/3 hour

So Total time = 4 + 2/3 = 4 2/3 hours

4.(2)

If the length and breadth of a rectangular are changed by x% and y% respectively .

the effective change in area = (x + y + xy/100)%

Here, x = -25. y = -25

so Percentage decrease (-25-25+25*25/100)%

= (-50+6.25)% = -43.75%

5. (1)

6. (4)

7. (2)

a/b = b/c => b^2 = ac

so a^4 : b^4 = a^4 : a^2c^2 = a^2:c^2

8. (2)

9. (4)

5x*6x = 120*HCF

30x^2 = 120*x

x = 4

10. (1)

Ratio of the values of coins = 3/1 : 5/2 : 7/4= 12:10:7

so value of the one rupee coins

= Rs. (12/29*145)= Rs.60 Number of One rupee coins