# Tips and Tricks of The Day

#### Record Limit :  10 20 30 50 100 200

2020-Nov-28
Ex: When x40 + 2 is divided by x4 +1, what is the remainder?

Trick:
Let f(x) = x40 + 2
Put x4 = –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
(l2 + b2 ) +2lb = 529
172 + 2lb = 529 => lb = 120
Area = l × b = 120 cm2
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 