Question

please tell the solution step by step. the answer in answer sheet is 60. please someone solve and tell. ASAP​

Answer 1

GIVEN :-

$\\ \sf \: \dfrac{p}{3} + \dfrac{p}{4} = 55 - \dfrac{p + 40}{5}$

TO FIND :-

• Value of p.

SOLUTION :-

$\\ \sf \: \dfrac{p}{ 3} + \dfrac{p}{4} = 55 - \dfrac{p + 40}{5}$

We will transpose -[(p+40)/5] to left hand side.

Since , it is in subtraction on right hand side , it will be in addition on left hand side.

$\\ \implies\sf \: \dfrac{p}{3} + \dfrac{p}{4} + \dfrac{p + 40}{5} = 55$

Now , we will add them by taking L.C.M.

L.C.M of [3,4,5] → 60

$\\ \implies \sf \: \dfrac{20(p) + 15(p) + 12(p + 40)}{60} = 55$

Now , we will transpose 60 to right hand side.

Since , 60 is in division on left hand side , it will be in multiplication on right hand side.

$\\ \implies \sf \: {20p + 15p + 12p + 480} = 55 \times 60 \\ \\ \implies \sf \: 47p + 480 = 3300$

Now , we will transpose 480 to right hand side .

Since it is in addition in left hand side , it will be in subtraction on right hand side.

$\\ \implies \sf \: 47p = 3300 - 480 \\ \\ \implies \sf \: 47p = 2820$

Now , we will transpose 47 on right hand side . Since , 47 is multiplied to p , it will be in division on right hand side.

$\\ \implies \sf \: p = \cancel \dfrac{2820}{47} \\ \\ \implies \underline{\underline{\boxed{ \bf \: \red{p = 60 }}}}$

Hence , value of p is 60.