**2020-Nov-28**

**Ex: When x**

^{40}+ 2 is divided by x^{4}+1, what is the remainder?**Trick:**

Let f(x) = x

^{40}+ 2
Put x

^{4}= –1,
f(x) = (–1)

^{10}+ 2 = 3**2020-Nov-25**

**Ex: What is the greatest number which will divide 110 and 128 leaving a remainder 2 in each case?**

**Trick:**

The greatest number = H.C.F. of (110 – 2) and (128 – 2)

= H.C.F. of 108 and 126 = 18

**2020-Nov-23**

**Ex: The sum of two numbers is 232 and their HCF is 29. What is the numbers of such pairs of numbers satisfied the above condition.**

**Trick:**

Let two number is 29a and 29b

29a + 29b = 232

a + b = 232/29 = 8

(a,b)= (1,7) (3,5)

The pair is (87, 145) (29,203)

**2020-Nov-20**

**Ex: The ratio of income of two persons P and Q was 6 : 7 last year. This year, the income of P is increased by 20% and that of Q by 40,000. If their income are now in the ratio of 24 : 25, the income of P was –**

**Trick:**

Let the population of P and Q be 6x and 7x respectively.

150x + 30x = 168x + 960000

12x = 960000

12x = 80000

x = 80000

Population of P was = 6 × 80000 = 480000

**2020-Nov-18**

**Ex: Jyoti sold an item for Rs. 8160 and incured a loss of 15%. At what price should she have sold the item to have gained of a profit of 25%?**

**Trick:**

Cost price = 8160 * 100 / 85 = 9600

Selling price to learn 25% profit

= 9600 * 125 / 100 = Rs. 12000

**2020-Nov-16**

**Ex: The ratio of milk and water in a mixture of 45 litre is 4: 1. If 3 litre more water should be added then what will be the new ratio of milk and water?**

**Trick:**

Milk : water = 1: 4

Sum of ratios = 1 + 4 = 5

Quantity of water in 45 litres of mixture = 45 × (1/5) = 9 litre

Quantity of milk in 45 litres of mixture = 45 × (4/5) = 36 litre

If 3 litre of water be added then new ratio becomes

= (9+3) : 36

= 12: 36

= 1: 3

**2020-Nov-11**

**Ex: The diagonal of a rectangle is 17 cm long and its perimeter is 46 cm. Find the area of the rectangle.**

**Trick:**

2(l+b) = 46

(l + b)

^{2}= (23)^{2}
(l

^{2}+ b^{2}) +2lb = 529
172 + 2lb = 529 => lb = 120

Area = l × b = 120 cm

^{2}**2020-Nov-09**

**Ex: The radius of a circle is twice the side of a square, whose area is 196 square meter. The length of rectangle is twice the diameter of circle. What is the perimeter of a rectangle if its breadth is half the length?**

**Trick:**

side of square = 14 m.

r = 28 m., l = 112 m, b = 56 m.

perimeter of rectangle = 2(112+56)= 336 m

**2020-Nov-04**

**Ex: Find the maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils.**

**Trick:**

910 = 2 × 5 × 7 × 13

1001 = 7 × 11 × 13

HCF = 91

**2020-Nov-02**

**Ex: Ramesh purchased an item of Rs. 80000 and sold it at a loss of 32% with this amount he purchased another item and sold it again at of 20% profit .What is his over all profit/loss ?**

**Trick:**

Ist SP = 8000 * 68 / 100 = Rs. 54400

IInd SP = 54400 * 120 / 1000 = Rs. 65280

Loss = 80000 - 65280 = Rs. 14720