Question

Mr Arun has rs 550 in the form of denominations of rs 10 and rs 50 if the no of 10 rupee notes is one more than that of the 50 rupee notes find the no of 10 rupee notes and 50 rupee notes

Answer 1

$\huge\mathfrak{Solution:}$

Let 50 rupees note be x and 10 rupees note be x+1

Now,

$\sf \: 50 \: rupee \: note = Rs \: 50x$

$\sf \: 10 \: rupee \: note = Rs \: 10(x + 1) = Rs \: 10x + 10$

According to the Question :

$\longrightarrow \sf \: 50x + 10x + 10 = 550$

$\longrightarrow \sf \:60x + 10 = 550$

$\longrightarrow \sf \:60x = 550 - 10$

$\longrightarrow \sf \:60x = 540$

$\longrightarrow \sf \:x = \dfrac{540}{60}$

$\longrightarrow \red{ \sf \:x =9 }$

Hence,

No. of 50 Rupee Note = 9

No. of 10 Rupee Note = (9+1) = 10

Amount :

$\sf \: 50 \: rupee \: note = Rs \: 50x = 50 \times 9 = \red{Rs \: 450}$

$\sf \: 10 \: rupee \: note = \sf \: Rs \: 10 x + 10 = 10(9) + 10 \\ \sf \:Rs \: 90 + 10 = \red{ Rs100}$

$\huge\mathfrak{Verification :}$

$\longrightarrow \sf \:Total \: (50 \: rupee \: note + 10 \: rupee \: note) \: = 550$

$\longrightarrow \sf \:450 + 100 = 550$

$\longrightarrow \sf \:550= 550$

Hence,Verified!

Answer 2

Answer:

$\large{\underline{\underline{\mathfrak\green{QuesTion:-}}}}$

Mr.Arun has Rs.550 in the form of denominations of Rs.10 and Rs.50.If the number of 10 rupees note is one more than that of the 50 rupee notes.Find the no.of 10 rupee notes and 50 rupee notes.

$\large{\underline{\underline{\mathfrak\pink{SoluTion:-}}}}$

Let number of Rs.50 notes be M.

$\therefore$ Number of Rs.10 notes = (M + 1)

$\therefore$ Denominations of Rs.50 = 50(M)

$\therefore$ Denominations of Rs.10 = 10(M + 1)

${\underline{\underline{\bold\green{ATQ:-}}}}$

$\rightharpoonup\sf 50(M) + 10(M + 1) = 550 \\\\\rightharpoonup\sf 50M + 10M + 10 = 550 \\\\\rightharpoonup\sf 60M = 550 - 10 \\\\\rightharpoonup\sf 60M = 540 \\\\\rightharpoonup\sf M = 540/60 \\\\\therefore\sf\green{M = 9 }$

$\rule{100}{2}$

$\mapsto\sf Number\: of \:Rs.50\: notes(M)$ = $\large{\boxed{\sf\green{9}}}$

$\mapsto\sf Number \: of \: Rs.10 \: notes (M+1)$=$\large{\boxed{\sf\green{10}}}$

VerifIcation:-

$\Rightarrow\sf 50(M) + 10(M + 1) = 550 \\\\\Rightarrow\sf 50(9) + 10(9 + 1) = 550 \\\\\Rightarrow\sf 450 + 100 = 550 \\\\\Rightarrow\sf 550 = 550 \: \: \: [Verified!]$