Question

please help me solve these two questions

Answer 1

The CP of one item be x
the sp of 16 items =20x
the profit =4x
the gain percent=4x/16x*100
=25%

a⁴+1/a⁴=119
a⁴+1/a⁴+2=119+2
(a²+1/a²)²=121
a²+1/a²=11
(a-1/a)²=9
a-1/a=3



a³-1/a³=(a-1/a)(a²+1/a²+1)
3*11=33

Answer 2

Heya user !!

43.
a⁴+1/a⁴ = 119

Adding 2 both sides

a⁴+1/a⁴+2(a)(1/a) = 119+2

a⁴+1/a⁴+2(a²)(1/a²) = 121

( a²+1/a² )² = 11²

a²+1/a² = 11

Subtracting 2 from both sides

a²+1/a²-2(a²)(1/a²) = 11-2

( a-1/a )² = 9

a-1/a = 3

Using formula -

(x-y)³=x³-y³-3xy(x-y)

(a-1/a)³=a³-1/a³-3(a)(1/a)(a-1/a)

3³=a³-1/a³-3(3)

Therefore, a³-1/a³=36 Ans.

42.
S.P. of 16 items = C.P. of 20 items

Let the cost price of 1 article be $x

C.P. of 20 items = $20

S.P. of 16 items = $20

➙S.P. of 1 item = $20/16 = $5/4 = $1.25

S.P. of 1 item > C.P. of 1 item
Hence, there is a Gain

Gain percentage = [S.P.-C.P./C.P]*100

=[1.25-1/1]*100

= 25%

Hence, correct answer is option (D)
I.e 25% Gain