Question

Anita has some coins with her. She has coins of Rs.10, Rs. 5 and Rs.1 in the ratio 2:3:5. The coins amount to a total of Rs. 960. Find the number of Rs.5 coins with Anita.
1) 36
2) 48
3) 64
4) 72
5) 84​

Answer 1

Given :

Anita has some coins with her. She has coins of Rs.10, Rs. 5 and Rs.1 in the ratio 2:3:5. The coins amount to a total of Rs. 960.

To find :

Find the number of Rs.5 coins with Anita.

Solution :

Let the number of coins with Anita be 2n, 3n and 5n

Now atq,

⇒ (2n * 10) + (3n * 5) + (5n * 1) = 960

⇒ 20n + 15n + 5n = 960

⇒ 40n = 960

⇒ n = 960/40

⇒ n = 24

Now number of coins :

Number of Rs. 10 coins = 2n = 2 * 24 = 48

Number of Rs. 5 coin = 3n = 3 * 24 = 72

Number of Rs. 1 coin = 5n = 5 * 24 = 120

Therefore,

Number of Rs. 5 coins = 72  [Option 4]

Answer 2

Answer :-

$\: \quad \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Ratios of the numbers has been used. We see that number of all the coins are given in ratio, then there will be a constant by which all are multiplied to make them in the original number. Even that constant is the factor by which they are divided. So, we will take the constant as variable and apply in question to get the answer.

Let's do it !!

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★ Formula Used :-

$\: \\ \: \large{\boxed{\boxed{\sf{2x(10) \: + \: 3x(5) \: + \: 5x(1)\: = \: \bf{960}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{\: Total \: value \: of \: each \: type \: of \: coin \: = \: \bf{Ratio \: part \: \times \: The \: value \: of \: x}}}}}$

$\: \\ \: \large{\boxed{\boxed{\sf{Number \: of \: Rs. \: 5 \: coins \: = \: \bf{3 \: \times \: x}}}}}$

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★ Question :-

Anita has some coins with her. She has coins of Rs.10, Rs. 5 and Rs.1 in the ratio 2:3:5. The coins amount to a total of Rs. 960. Find the number of Rs.5 coins with Anita.

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★ Solution :-

Given,

» Ratio of the coins = 2 : 3 : 5

• Let the constant by which all the number of coins should be multiplied be 'x'. Then,

$\: \\ \: \large{\sf{\longrightarrow \: \: \: Total \: value \: of \: each \: type \: of \: coin \: = \: \bf{Ratio \: part \: \times \: The \: value \: of \: x}}}$

» Value of Rs. 10 coins = 2x

» Value of Rs. 5 coins = 3x

» Value of Rs. 1 coins = 5x

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~ For the value of x :-

We are given, the coins of each denominations. We see if we know the value of each type of coin and add them then that will be equal to the total value. Then,

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: (Value \: Rs. \: 10 \: coin) \: + \: (Value \: of \: Rs. \: 5 \: coin) \: + \: (Value \: of \: Rs. \: 1 \: coin) \: = \: \bf{Total \: Value}}}$

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: 2x(10) \: + \: 3x(5) \: + \: 5x(1) \: = \: \bf{960}}}$

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: 40x \: = \: \bf{960}}}$

$\: \\ \: \large{\sf{\Longrightarrow \: \: \: x \: = \: \bf{\dfrac{\cancel{960}}{\cancel{40}}} \: \: = \: \: \underline{\underline{24}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Value \: of \: x \: = \: \bf{24}}}}}$

~ For the Total Value of Each Type of Coins :-

» No. of Rs. 10 coins = 2x = 2(24) = 48

» No. of Rs. 5 coins = 3x = 3(24) = 72

» No. ot Rs. 1 coins = 5x = 5(24) = 120

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$\: \\ \: \: \large{\boxed{\boxed{\tt{Number \: of \: Rs. \: 10 \: coins\: = \: \bf{48}}}}}$

$\: \: \: \large{\boxed{\boxed{\tt{Number \: of \: Rs. \: 5 \: coins\: = \: \bf{72}}}}}$

$\: \: \: \large{\boxed{\boxed{\tt{Number \: of \: Rs. \: 1 \: coins\: = \: \bf{120}}}}}$

$\: \: \\ \large{\underline{\underline{\rm{\leadsto \: \: Thus \: the \: number \: of \: Rs.\: 5 \: Coins \: are \: \: \boxed{\bf{72 \: coins \: \: : \: \sf{Option \: 4}}}}}}}$

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$\: \: \large{\underbrace{\rm{Aid \: to \: Memory \: :-}}}$

• Total value of Rs. 10 coins = 10 × 48 =

Rs. 480

• Total value of Rs. 5 coins = 5 × 72 =

Rs. 360

• Total value of Rs. 1 coins = 1 × 120 =

Rs. 120

This satisfies that :-

=> Rs. 480 + Rs. 360 + Rs. 120 = Rs. 960

So the situation confirms to be true , hence our answer is correct.

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