Question

A bag contain 25 paise, 50 paise and ₹1
coins in the ratio of 2 :3 : 5 and it amounts
to 385. Find the number of coins of each
type.​

Answer 1

Answer:

There are 110 coins of 25 paise coins, 165 coins of 50 paise coins and 275 coins of Rs. 1.

Step-by-step explanation:

$\textbf{\underline{\underline{Given :}}}$

The bag contains = 25 paise ; 50 paise and Rs. 1 coins

Ratio = 2 : 3 : 5

Total amount = Rs. 385

$\textbf{\underline{\underline{To find :}}}$

The number of coins of each type

$\textbf{\underline{\underline{Solution : }}}$

$\textsf{Let the coins be -}$

• $\textsf{25 paise = 2y }$
• $\textsf{50 paise = 3y}$
• $\textsf{Rs. 1 = 5y }$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{According to the question -}}}$

The total count is Rs. 385,

25 paise is the $\sf{\dfrac{1}{4}}$ of a rupee, so the value of coins would be $\sf{\dfrac{2y}{4}}$

50 paise is the $\sf{\dfrac{1}{2}}$ of a rupee, so the value of coins would be $\sf{\dfrac{3y}{2}}$

$\sf{\longrightarrow} \: \dfrac{2y}{4} + \dfrac{3y}{2} + 5y = 385 \\ \\ \sf{\longrightarrow} \: \dfrac{2y}{4} + \dfrac{3y}{2} + \dfrac{5y}{1} = 385 \\ \\ \sf{\longrightarrow} \: \dfrac{2y + 6y + 20y}{4} = 385 \\ \\ \sf{\longrightarrow} \: \dfrac{28y}{4} = 385 \\ \\ \sf{\longrightarrow} \: 28y = 385 \times 4 \\ \\ \sf{\longrightarrow} \: 28y = 1540 \\ \\ \sf{\longrightarrow} \: y = \dfrac{1540}{28} \\ \\ \sf{\longrightarrow} \: y = 55$

$\rule{300}{1.5}$

✯ $\textsf{\underline{Number of {\blue{25 paise}} coins -}}$

$\sf{\longrightarrow} \: 2y = 2(55) = 110 \: coins$

✯ $\textsf{\underline{Number of {\blue{50 paise}} coins - }}$

$\sf{\longrightarrow} \: 3y = 3(55) = 165 \: coins$

✯ $\textsf{\underline{Number of {\blue{1 rupee}} coins -}}$

$\sf{\longrightarrow} \: 5y = 5(55) = 275 \: coins$

$\therefore$ There are 110 coins of 25 paise coins, 165 coins of 50 paise coins and 275 coins of Rs. 1.

Answer 2

||✪✪ QUESTION ✪✪||

A bag contain 25 paise, 50 paise and ₹1

coins in the ratio of 2 :3 : 5 and it amounts

to 385. Find the number of coins of each

type. ?

|| ✰✰ ANSWER ✰✰ ||

Given that, bag have 25 paise, 50 paise and ₹1 coins in the ratio of 2 :3 : 5...

So, Lets assume that, 25 paise coins are 2x , 50 paise coins are 3x and Rs.1 coins are 5x..

→ 25 paise = 25/100 = 1/4 Rs.

→ 50paise = 50/100 = 1/2 Rs.

Now, given Total amount is Rs.385,

So,

→ (1/4) * 2x + (1/2) * 3x + 1 * 5x = 385

→ (x/2) + (3x/2) + 5x = 385

Taking LCM,

→ (x + 3x + 10x) /2 = 385

→ 14x = 385*2

→ 14x = 770

Dividing both sides by 14,

→ x = 55

So,

→ 25 paise coins are 2x = 2*55 = 110

→ 50 paise coins are 3x = 3*55 = 165

→ Rs.1 coins are 5x = 5*55 = 275.

Hence, 25 paise coins, 50 paise coins and Rs1, coins are 110, 165 and 275 Respectively.