Question

A bag contains 10 coins of ₹ 2 and 50 p denomination. Find the number of coins of each denomination, if the total amount in the bag is ₹ 14.​

Answer 1

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• A bag has 10 coins of ₹ 2 and 50p .
• The total value of money is ₹ 14.

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• The number of each types of coins.

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } HoW\:To\:SolvE\:?}}}}}$

Here we will frame a linear equⁿ in one variable or in two variables . Then we will write the given conditions mathematically and try to solve the equⁿ to get the required answer

$\Large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Given that a bag contains 10 coins of ₹ 2 and 50 p denomination. The total amount in the bag is ₹ 14.

So , let us take ,

• $\sf Number\:of\:Rs2\:coins\:be\:x.$
• $\sf Number\:of\:50p\: coins\:be\:(10-x)$

Now , if Number of Rs 2 coins is x , its value will be Rs 2x .

Similarly if Number of 50p = Rs½ is (10-x) , its value will be Rs ½ (10 - x) .

$\underline{\purple{\orange{\leadsto}\mathscr{A}\sf{ccording}\:\:\mathscr{T}\sf{o}\:\:\mathscr{Q}\sf{usetion}:-}}$

$\tt:\implies \cancel{Rs} 2\times x +\dfrac{\cancel{Rs}1}{2}\bigg(10-x\bigg)=\cancel{Rs}14$

$\tt:\implies 2x-\dfrac{x}{2}+\dfrac{\cancel{10}}{\cancel{2}}=14$

$\tt:\implies 2x -\dfrac{x}{2}+5=14$

$\tt:\implies \dfrac{4x-x}{2}=14-5$

$\tt:\implies \dfrac{3x}{2}=9$

$\tt:\implies x=\dfrac{\cancel{9}\times2}{\cancel3}$

$\underline{\boxed{\red{\tt{\longmapsto\:\:x\:\:=\:\:6}}}}$

$\bf Hence\: required\: Number\:of\:coins$

• $\tt Rs 2 = x = \pink{6}$
• $\tt 50p = (10-x) = (10-6) =\pink{4}$

$\orange{\boxed{\blue{\bf{\green{\dag }Hence\:no.\:of\:Rs2\:coins\:is\:6\:\&\:50p\:coins\:is\:4.}}}}$