Question

I have a total of Rs 300 in coins of denomination Rs 1,Rs 2 and Rs 5.The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?​

Answer 1

$\large{\underline{\sf{\red{Required\:Answer:}}}}$

• Number of Re 1 coins = $\large\boxed{\underline{{\sf 80 }}}$

• Number of Rs 2 coins = $\large\boxed{\underline{{\sf 60 }}}$

• Number of Rs 5 coins = $\large\boxed{\underline{{\sf 20 }}}$

Given:-

• No. of Rs 5 coins + No. Rs of 2 coins + No. Rs of 1 coin = Rs 160.

• Number of Rs 2 coins is 3 times the number of Rs 5 coins.

• Total amount = Rs 300.

To Find:-

• Number of coins in each domination.

Solution:-

Let the number of Rs 5 coins be x.

Then,

Number of Rs 2 coins = 3x

Number of coins of Re 1:-

$\purple{\implies\:\:}$ $\rm{160-(x+3x)}$

$\purple{\implies\:\:}$ $\rm{160-4x}$

According to the question :-

$\green{\implies\:\:}$ $\rm{5 \times x+2\times 3x+1 \times(160-4x)=300}$

$\green{\implies\:\:}$ $\rm{5x+6x+160-4x=300}$

$\green{\implies\:\:}$ $\rm{11x + 160 - 4x = 300}$

$\green{\implies\:\:}$ $\rm{7x + 160 = 300}$

$\green{\implies\:\:}$ $\rm{ 7x = 300 - 160}$

$\green{\implies\:\:}$ $\rm{ 7x = 140}$

$\green{\implies\:\:}$ $\rm{  x = \dfrac{140}{7}}$

$\green{\implies\:\:}$ $\rm{  x = 20 }$

Hence,

❍ Number of coins of Rs 5 denomination

                         → 20

❍ Number of coins of Rs 2 denomination

                  → 3 × 20 = 60

❍ Number of coins of Rs 2 denomination

                → 160 - (4 × 20)

                → 160 - 80 = 80

____________________________

Answer 2

Answer:

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: given \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Total amount = Rs 300

(Rs 1,Rs 2, Rs 5)

• The number of Rs 2 coins is 3 times the number of Rs 5 coins.

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: To\: find \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• No. of coins in each denomination

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Let, \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Number of Rs5 coins be x
• Number of Rs 2 coins = 3× Number of 5 Rs coins =3x
• Number of Rs 1 coins = 160−(x+3x)

=160−4x

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Now\: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Amount of Rs5 coins =5×x=5x
• Amount of Rs2 coins =2×3x=Rs6x
• Amount of Re1 coins =(160−4×x)

=160−4x

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Solution \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

Now, according to Question,

• Total amount =Rs300

$\\ \\ \large \rm\bold{= > 160 - 4x + 5x + 6x = 300} \\ \large \rm \bold{ = > 7x = 300 - 160} \\ \large \rm \bold{ = > x = \cancel\frac{140}{7} } \\ \large \rm\bold{ = > x = 20}$

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Now \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• Number of Re 1 coins =160−4x

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ=160−4×20

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ=80

• Number of Rs2 coins =3x=3×20=60
• Number of Rs5 coins =x=20

$\large \bigstar \bf {\underbrace{ \color{navy}{ \: \: \: \: \: \: \: \: \: \: Therefore \: \: \: \: \: \: \: \: \: \: \: }} }\bigstar$

• The number of 1 Rs coin = 80
• The number of 2 Rs coins = 60
• The number of 5 Rs coins = 20