PROFIT C1

 

A man got a profit of 200/= after selling an item for 8000/=. Find the percentage profit.

 

Solution

 

%’ge profit = Profit   X  100    where B. P. represents Buying Price.

                    B.P

 

%’ge profit = 200   X  100   

                   8000

 

 

 

%’ge profit = 2   X  100   

                         80

 

 

%’ge profit = 200   

                    80

 

 

%’ge profit = 2.5%   

                       

Hence Percentage Profit is 2.5%

 

TRY THIS………………….

 

A man got a profit of 300/= after selling an item for 24000/=. Find the percentage profit.

FACTORS C1

 

Evaluate 545 x 237 + 463 x 545.

 

Solution

 

= 545 x 237 + 463 x 545

 

= 545 x (237 + 463)

 

= 545 x 700

 

= 381500

 

Hence 545 x 237 + 463 x 545 = 381500

 

TRY THIS………….

 

 

Evaluate 496 x 292 + 708 x 496.

ARITHMETIC PROGRESSION H7

 

The 1st term of an A.P. is 80 and the common difference is 29. Find the 10th term.

 

Solution

 

A₁= 80, d = 29

 

A_n = A₁ + (n-1)d

 

A₁₀ = A₁ + (10-1)d

 

A₁₀ = A₁ + 9d

 

A₁₀ = 80 + (9x29) [ after substituting A₁= 80, d = 29 as given above]

 

∴ A₁₀ = 80 + 261

 

A₁₀ = 341

 

Hence the 10th term is 341.

 

  

TRY THIS……………

 

The 1st term of an A.P. is 55 and the common difference is 160. Find the 12th term.

LOGARITHMS J3

Evaluate Log10,000,000,000 -  log 0.0001 + log₃243 -  log 0.001

 

Solution

 

= Log10,000,000,000 -  log 0.0001 + log₃243 -  log 0.001

 

= Log₁₀10¹⁰ -  log₁₀ 10^-4 + log₃3⁵-  log₁₀ 10^-3    243=

 

= 10Log10 -  (-4log 10) + (5log₃3) -  (-3log 10)

 

= (10x1) - (-4x1) + (5x1) - (-3x1)

 

= 10 - (-4) + (5) - (-3)

= 10 + 4  +  5 + 3

= 14 + 8

= 22 answer

 

Hence Log10,000,000,000 -  log 0.0001 + log₃243 -  log 0.001=22 

 

TRY THIS……………..

 

 

Evaluate Log100,000,000,000  -  log 0.000001 + log₃81 -  log 0.001

GEOMETRY J3

 Find the midpoint of a line from (3, 12) to (5, 20)

Solution

x1=3, x2=5, y1=12,y2=20.

Mid point = (x1 + x2, y1 + y2)

                         2           2

Mid point = (3 + 5,  12 + 20)

                         2          2

Mid point = (8, 32)

                     2    2

Hence midpoint = (4, 16)

TRY THIS……………………..

Find the midpoint of a line from (-9, 18) to (17, -4)

BINARIES J1

p*q =(p-q)(6p+q) Find (2*-3)

solution

=(p-q)(6p+q)

=[2-(-3)][(6x2)+(-3)]

=[2+3][12+(-3)]

=(5)(9)

=45

Hence (2*-3) = 15

TRY THIS……………….

 

 If p*q =(5p-q)(6p+q) Find (3*-4)

 

GP J1

 

The 1st term of a geometric progression is 2 and the 5th term is 512. Find the common ratio.

 

Solution

 

G₁=2, G₅=512, n=5

 

G_n = G₁r^n-1;

 

G₅ = G₁r^5-1;

 

G₅ = G₁r⁴;

 

512 = 2 x r⁴;

 

512 = 2r⁴;

 2       2

 

256 = r⁴;  Finding the fourth root of 256,

We do prime factorization of 256.

 

2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

 

 

 

 

 

 

 

 

 

 

 

4⁴ = r⁴;  [equal powers will cancel out]

 

4 = r

 

r = 4

 

 

Hence the common ratio is 4.

 

TRY THIS …………..

The 1st term of a geometric progression is 3 and the 5th term is 9375. Find the common ratio.