Question

If $ A=P+\dfrac{PRT}{100} $ , make T the subject of the formula . When A = 500 , P= 400 and T = 10, find R.

Answer 1

Hint: As in the given question We need to make T as a subject of the formula, it means we only need to keep T as in one side of the formula and the rest of the variables on the other side of the formula.
Then we can substitute the value of the variable in formula to get the value of R.

Complete step-by-step answer:
Given formula is $ A=P+\dfrac{PRT}{100} $ ……………………………………..(i)
On subtracting P from both side
 $ \Rightarrow A-P=P-P+\dfrac{PRT}{100} $
 $ \Rightarrow A-P=\dfrac{PRT}{100} $
On multiplying 100 both side
 $ \Rightarrow (A-P)\times 100=\dfrac{PRT}{100}\times 100 $
 $ \Rightarrow (A-P)\times 100=PRT $
On dividing PR from both sides.
 $ \Rightarrow \dfrac{(A-P)\times 100}{PR}=T $
So required formula for T is
 $ \Rightarrow T=\dfrac{(A-P)\times 100}{PR} $
On substituting A = 500, P= 400 and T = 10 in equation (i)
 $ \Rightarrow 500=400+\dfrac{400\times R\times 10}{100} $
 $ \Rightarrow 500-400=\dfrac{400\times R\times 10}{100} $
 $ \Rightarrow 100=\dfrac{400\times R\times 10}{100} $
 $ \Rightarrow 100\times 100=400\times R\times 10 $
 $ \Rightarrow R=\dfrac{100\times 100}{400\times 10} $
 $ \Rightarrow R=2.5 $
Hence the required value of R is 2.5.

Note:If we need to make any particular variable in formula as a subject it means we need to solve the formula for that variable. In this we need to remember that we need to find the value of R after substituting given values of A , P and T. But we made T as a subject from the given formula. So we need to be careful about it otherwise by mistake we can find the value of T .