Question

someone pls help really important​

Answer 1

Answer:

Step-by-step explanation:

6. Let the number of 10 rupee notes be x.

   Let the number of 5 rupee notes be y.

Given, sum of 10 rupee notes and 5 rupee notes is equal to 190.

=> x * 10 + y * 5 = 190

=> 10x  + 5y = 190  ----- (i)

Given, if number of notes interchange the sum is 185

=> y * 10 + x * 5 = 185

=> 10y + 5x = 185 --- (ii)

Multiply (i) by 2 and then subtract (ii) from it, to solve the equations.

20x + 10y = 380

5x + 10y   =  185

-       -          -

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15x = 195

=> x = 195/15 = 13.

=> x = 13

Substitute value of x in any of  (i) or (ii) to get y.

substituting in (i),  10 * 13 + 5y = 190

                             => 5y = 190 - 130

                             => 5y = 60

                             => y = 12.

Thus the number of 10 rupee notes are 13.

        the number of 5 rupee notes are 12.

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7. Since points (3, -1) and (6,1) lie on the line px + qy = 9, substituting these values in place of x and y should make L.H.S and R.H.S equal.

=> Substituting (3, -1),  3p - q = 9  --- (i)

=> Substituting (6,1), 6p + q = 9  ---  (ii)

Now solve equations (i) and (ii) by addition.

3p - q = 9

6p+q = 9

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9p = 18

=> p = 18/9 = 2.

Substitute value of p in any of the equations.

substituting in (i), 3 * 2 - q = 9

                           => 6 - q = 9

                           => q = 6 - 9 = -3.

Thus the equation is 2x - 3y = 9.

Verification: Substitute the (3, -1 ) and (6,1) in place of x and y. The L.H.S of equation will be equal to R.H.S

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8. Let x and y be the two numbers.

Given, sum of two numbers divided by 15, quotient = 2, remainder = 10.

=> 15 * 2 + 10 = x + y

=> x + y = 40  ---- (i)

Given, difference of two numbers divided by 3, quotient = 4, remainder = 2.

=> 3 * 4 + 2 = x - y

=> x - y = 14  ---- (ii)

Solve equations (i) and (ii) by addition,

x + y = 40

x - y = 14

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2x = 54

=> x = 54/2 = 27.

Substitute value of x in any of the equations to get y.

Substituting in (i),

=> 27 + y = 40

=> y = 40 - 27

       = 13.

Thus the numbers are 27 and 13.          

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