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

### Set A

1.If the difference of the squares of two natural numbers is 37, then the sum of the squares of the numbers will be

(1) 690

(2) 687

(3) 685

(4) 672

2.The smallest number to be subtracted from 4750 so as to get a perfect square number is

(1) 126

(2) 162

(3) 216

(4) 612

3.A cricket player has an average score of 30 runs for 42 innings played by him. In an innings, his highest score exceeds his lowest score exceeds his lowest score by 100 runs. If these two innings are excluded, his average of the remaining 40 innings is 28 runs. His highest score in an innings is

(1) 125

(2) 120

(3) 110

(4) 100

4.The average of four consecutive even numbers is 27. The largest of these number is

(1) 28

(2) 26

(3) 32

(4) 30

5.The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly salary of 7 technicians is Rs.10,000 and average monthly salary of the rest is Rs. 7,800, the total number of workers in the workshop is

(1) 18

(2) 20

(3) 22

(4) 24

6.In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is

(1) 1 : 2

(2) 3 : 4

(3) 1 : 4

(4) 3 : 5

7.If A’s salary is 25% more than B’s salary, then B’s salary is how much lower than A’s salary?

(1) 33 1/3%

(2) 25%

(3) 20%

(4) 16 2/3%

8.Rs. 366 are to be divided amongst A, B and C so that A may get 1/2 as much as B and C together and B may get 2/3 as much as A and C together. A’s share will be

(1) Rs. 120

(2) Rs. 122

(3) Rs. 124

(4) Rs. 128

9.Ram and Gopal have money in the ratio 7 : 17 and Gopal and Krishna also have money in the same ratio 7 : 17. If Ram has Rs. 490, Krishna has

(1) Rs. 2,330

(2) Rs. 2,680

(3) Rs. 2,890

(4) Rs. 3,000

10.The ratio of the principal and its yearly amount is 8 : 9. What is the rate of simple interest per annum?

(1) 12%

(2) 12 1/2%

(3) 10%

(4) 10 1/2%

Answers and Solution:

1.(3) Let the number be x and y

x > y ∴ x^2-y^2 = 37

= (x+y) (x-y) = 37×1

= x+y = 37 and x-y = 1

∴ x^2+y^2 = ((x+y)^2+(x-y)^2 )/2

=((37)^2+(1)^2)/2

= 685

2.√4750 = 68.9

68×68 = 4624

∴ Required Number = 4750 – 4624

= 126

3.(4)

4.(4) Second Number = Average – 1

= 26

∴ Fourth number = 26+4 = 30

5.(3)Let the total number of worker in the workshop be X.

∴ 8500* x = 10000*7+(x-7)*7800

= 8500x-7800x = 70000-54600

= 700x = 15400

∴ x = 22

6.(2) Boys : Girls = 6 : 5

∴ Girls = 6/11×66=36

Boys = 30

New ratio = 30 : (36+4)

= 30 : 40

= 3 : 4

7.(3)

8.(2)

9.(3) Ram : Gopal = 7 : 17

Gopal : Krishna = 7 : 17

∴ Ram Krishna = 7/17 × 7/17 = 49/289

∴ Amount with Krishna = 289/49 × 490

= 2890

10.(2)

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

### Set B

1.With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5 After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is

(1) 4%

(2) 6%

(3) 5%

(4) 7%

2.Rs, 1,000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 2,000 after

(1) 15 years

(2) 18 years

(3) 20 years

(4) 16 2/3 years

3.A pen is listed for Rs. 12. A discount of 15% is given on it. A second discount is given bringing the price down to Rs. 8.16. The rate of second discount is

(1) 20%

(2) 15%

(3) 18%

(4) 25%

4.A sum of money amounts to Rs. 5,200 in 5 years and to Rs. 5,680 in 7 years at simple interest. The rate of interest per annum is

(1) 3%

(2) 4%

(3) 5%

(4)6 %

5.A borrows Rs. 800 at the rate of 12% per annum simple interest and B borrows Rs. 910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal?

(1) 18

(2) 20

(3) 22

(4) 24

6.A person deposited Rs. 400 for 2 years, Rs. 550 for 4 years and Rs. 1,200 for 6 years. He received the total simple interest of Rs. 1,020. The rate of interest per annum is

(1) 10%

(2) 5%

(3) 15%

(4) 20%

7.The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on the set of the total discount on the set of the shirt and trousers is 30%, the discount, offered on the trousers is

(1) 15%

(2) 20%

(3) 25%

(4) 30%

8.A dealer buys an article marked at Rs. 25,000 with 20% and 5% off. He spends Rs. 1,000 for its repairs and sells it for Rs. 25,000. What is his gain or loss per cent?

(1) Loss of 25%

(2) Gain of 25%

(3) Gain of 10%

(4) Loss of 10%

9.A company offers three types of successive discounts : (i) 25% and 15%, (ii) 30% and 10%. (iii) 35% and 5%. Which offer is the best a customer?

(1) First offer

(2) Second offer

(3) Third offer

(4) Any one : all are equally good

10.An article is listed at Rs. 900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single discount of 16%, instead of two discounts?

(1) Gain of Rs. 4,76

(2) Loss of Rs. 5,76

(3) Gain of Rs. 5,76

(4) Loss of Rs. 4.76

Answers and Solution:

1. (3)

Let the period of time be T years.Then,

(400*5*T)/100 = (500*4*6.25)/100

=> T = 6 (1/4)

2. (4)

3. (1)

Let the rate of second discount = x%

After 15% discount

Price of pen = 85/100 * 12

= Rs. 10.20

Now, 10.20 - 8.16 = Rs.2.04

it is second discount .

so x/100 *10.20 = 2.04

=> 10.2x = 204

=> x = 204/10.2 = 20

4. (4)

5. (3)

Let the period of time be T years.

so 880 + (800*12*T)/100

= 910+ (910*10*T)/100

=> 800 + 96T = 910 + 91T

=> T = 110/5 = 22 years

6.(1)

7. (3)

Let the marked price of shirt be Rs. x and that of trousers be Rs. 2x

Let the discount on the trosers be y % Then,

x*40/100 + 2x*y/100 = 3x *30/100

=> 40x + 2xy = 90x

=> 2y = 90 - 40 => y = 50/2 = 25%

8. (2)

9. (3)

10. (2)

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