Question

Answer the question step by step

Answer 1

Let the Number of One Rupee coins in the Bag be : A

Let the Number of 50 Paise coins in the Bag be : B

Let the Number of 25 Paise coins in the Bag be : C

☢  Ratio of Number of 1 Rupee coins to that of 50 Paise coins is 5 : 9

$\mathsf{:\implies \dfrac{A}{B} = \dfrac{5}{9}}$

$\mathsf{:\implies A = \dfrac{5B}{9}}$

☢  Ratio of Number of 50 Paise coins to that of 25 Paise coins is 2 : 1

$\mathsf{:\implies \dfrac{B}{C} = \dfrac{2}{1}}$

$\mathsf{:\implies C = \dfrac{B}{2}}$

Given : Total value of the coins in the bag is Rs. 425

It means : Sum of Total value of 1 Rupee coins and Total value of 50 Paise coins converted into Rupees and Total Value of 25 Paise coins converted into Rupees should be equal to Rs. 425

$:\implies$  A (rupees) + B (50 paise's) + C ( 25 paise's) = 425

But, B and C are in Paise's. So, We need to convert them into Rupees

$\mathsf{\bigstar\;\;We\;know\;that : 50\;paise = \dfrac{Rupee}{2}}$

$\mathsf{\bigstar\;\;We\;know\;that : 25\;paise = \dfrac{Rupee}{4}}$

$\mathsf{:\implies A\;(rupees) + B\left[\dfrac{1}{2}\right]\;(rupees) + C\left[\dfrac{1}{4}\right]\;(rupees) = 425}$

$\mathsf{:\implies A + \dfrac{B}{2} + \dfrac{C}{4} = 425}$

As we need only the value of 50 paise coins in the bag, convert the above equation in terms of B by substituting the value's of A and C in terms of B

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{B}{2} + \dfrac{\dfrac{B}{2}}{4} = 425}$

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{B}{2} + \dfrac{B}{8} = 425}$

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{4 \times B}{4 \times 2} + \dfrac{B}{8} = 425}$

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{4B}{8} + \dfrac{B}{8} = 425}$

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{4B + B}{8} = 425}$

$\mathsf{:\implies \dfrac{5B}{9} + \dfrac{5B}{8} = 425}$

★  Least Common Multiple of 9 and 8 is 72

$\mathsf{:\implies \dfrac{5B(8) + 5B(9)}{72} = 425}$

$\mathsf{:\implies \dfrac{40B + 45B}{72} = 425}$

$\mathsf{:\implies \dfrac{85B}{72} = 425}$

$\mathsf{:\implies \dfrac{B}{72} = \dfrac{425}{85}}$

$\mathsf{:\implies \dfrac{B}{72} = 5}$

$:\implies$  B = (72 × 5)

$:\implies$  B = 360

It means : Total Number of 50 Paise coins in the Bag are : 360

$:\implies \mathsf{Value\;of\;50\;Paise\;Coins\;in\;the\;Bag = 360 \times \dfrac{1}{2}\;Rupees}$

$:\implies \mathsf{Value\;of\;50\;Paise\;Coins\;in\;the\;Bag = 180\;Rupees}$

Answer : Option (2)

Answer 2

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