**1.A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is :**

**2.If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their squares is:**

**3.If ⋆ is an operating such that x ⋆ y = 3x + 2y, then 2 ⋆ 3 + 3 ⋆ 4 is equal to :**

**4.In a school, the average age of students is 6 years, and the average age of 12 teachers is 40 years. If the average age of the combined group of all the teachers and students is 7 years, then the number of students is :**

**5.The average age of 30 boys in a class is 15 years. One boy aged 20 years, left the class, but two new boys came in his place whose ages differ by 5 years. If the average age of all the boys now in the class still remains 15 years, the age of the younger newcomer is :**

**6.Given that 10% of A’s income = 15% of B’s income = 20% of C’s income. If sum of their income is Rs. 7800. Then B’s income is :**

**7.If two numbers are respectively 20% and 50% of a third number, what is the ratio between the two numbers ?**

**8.If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to**

**9.Two numbers are in the ratio 2 : 3. If 2 is subtracted from the first and 2 is added to the second, the ratio becomes 1 : 2. The sum of the numbers is :**

**10.The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs, 2600 and Rs. 1800 respectively, their incomes are :**

**Answers and Solution:**

1. (2)

Number = 269*68

= 269 * (67+1)

= 269 * 67 + 269

clearly,remainder is obtained on dividing 269 by 67 that is 1.

2. (4)

Let x+y = 20 and x-y = 8

S0 (x+y)(x-y) = 20*8

=> x^2-y^2 = 160

3. (2)

Here x*y = 3x+2y

so 2*3+3*4 = (3*2+2*3)+(3*3+2*4)

= 12+17=29

4. (1)

Let the number of students be x.then,

=> 7 = (x*6+12*40)/(x+12)

=7x + 84 = 6x + 480

=> x = 396

5. (2)

6. (3)

10% of A = 15% 0f B = 20* 0f C

=> 10A = 15B = 20C

=> 10A/60 = 15B/60 = 20C/60

=> A/6 = B/4 = C/3

So A : B : C = 6 : 4 : 3

so 6x + 4x + 3x = 7800

=> 13x = 7800

x = 600

B’s income = 4x = 600*4 = 2400

7.(2)

8. (4)

9. (1)

10. (1)

Let the incomes of two persons be Rs.5x and 3x rupess and their expenditure be Rs.9x and 5x respectively,

As given

5x – 9y = 2600…….(1)

3x – 5y = 1800…….(2)

by solve

then, x = 1600

So First person’s income = 1600*5 = 8000

Second’s person income = 1600*3 = 4800