Question

1 point
5. Nikhil has Rs. 500 with him in Rs
10 and Rs 5 notes. He has 3 times as
many Rs. 5 notes as he has Rs 10
notes. How much money of Rs 5
denomination does he have?
Rs. 200
Rs.500
Rs 300
Rs 150​

Answer 1

Let :

• Number of Rs5 notes = x
• Number of Rs10 notes = y

Given :

• Nikhil has Rs 500
• Number of Rs5 notes = 3 times number of Rs 10

To find :

Amount of money he has Rs5 notes.

Solution :

• Amount of money Nikhil has as Rs5 = 5× Number of Rs5 notes

➝ Amount of money Nikhil has as Rs5 = 5x

• Amount of money Nikhil has as Rs10 = 10 × Number of Rs10 notes

➝ Amount of money Nikhil has as Rs10 = 10y

• Therefore total amount of money = Amount of money Nikhil has as Rs5 + Amount of money Nikhil has as Rs10

➝ Total amount of money = 5x + 10y

➝ 5x + 10y = 500 equation 1

_______________________________________________

Also, according to question

Number of Rs5 notes = 3× Number of Rs10 notes

➝ x = 3y

➝ y = x/3 equation 2

_______________________________________________

On putting value of y from equation 2 into equation 1 we get;

$\sf \implies \: 5x \: + \: 10 \bigg( \dfrac{x}{3 \: } \bigg) \: = 500 \\ \\ \sf \implies \: 5x \: + \: \dfrac{10x}{3 \: } \: = 500 \\ \\ \sf \implies \: \dfrac{(5x \times 3) + (10x \times 1)}{3 \: } \: = 500 \\ \\ \sf \implies \: \dfrac{15x + 10x }{3 \: } \: = 500 \\ \\ \sf \implies \: \dfrac{25x }{3 \: } \: = 500 \\ \\ \sf \implies \:25x = 500 \times 3 \\ \\ \sf \implies \:x \: = \: \dfrac{1500}{25} \\ \\ \sf \implies \:x \: = \: \bold{60}$

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This gives number of Rs5 notes = 60

➝ Amount of money Nikhil has as Rs5 = 5x

➝ Amount of money Nikhil has as Rs5 = 5×60

➝ Amount of money Nikhil has as Rs5 = Rs300

_______________________________________________

ANSWER :

Option 3) Rs 300

Answer 2

A N S W E R :

• Option (c) is correct
• Rs. 300

Let do it,

• Number of Rs. 5 notes = x
• Number of Rs. 10 notes = y

Given :-

• Nikhil has Rs. 500
• Number of Rs. 5 notes = 3 times
• Number of Rs. 10

To find :-

• Find the amount of money he has Rs. 5 notes ?

Solution :-

• Amount of money Nikhil has as Rs. 5 = 5x Number of Rs. 5 notes.

$\large\dashrightarrow$Amount of money Nikhil has as Rs. 5 = 5x

• Amount of money Nikhil has as Rs. 10 = 10x Number of Rs. 10 notes.

$\large\dashrightarrow$Amount of money Nikhil has as Rs. 10 = 10y

$\large\therefore$Total Amount of money = Amount of money Nikhil has as Rs. 5 + Amount of money Nikhil has as Rs. 10

$\large\dashrightarrow$Total Amount of money = 5x + 10y

$\large\dashrightarrow$5x + 10y = 500 equation 1

★ According to question :

• Number of Rs. 5 notes = 3x number of Rs. 10 notes.

$\large\dashrightarrow$x = 3y

$\large\dashrightarrow$y = $\large{\sf{\frac{x}{3}}}$ equation 2

$\large\star$On putting value of y from equation 2 into equation 1

We get,

Now,

:$\implies$5x + 10 $\large{\sf\bigg( {\frac{x}{3}\bigg)}}$= 500

$~~~~~$:$\implies$5x + $\large{\sf{\frac{10x}{3}}}$= 500

$~~~~~~~~~~$:$\implies$$\large{\sf{\frac{(5x \times 3) + (10x \times 1)}{3}}}$= 500

$~~~~~~~~~~~~~~$:$\implies$$\large{\sf{\frac{15x + 10x}{3}}}$= 500

$~~~~~~~~~~~~~~~~~~~$:$\implies$$\large{\sf{\frac{25x}{3}}}$= 500

$~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$25x = 500 × 3

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = $\large{\sf{\frac{1500}{25}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = ${\cancel{\dfrac{1500}{25}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{x~=~60}}}}}$★

V E R I F I C A T I O N :

Number of Rs. 5 notes = 60

$\therefore$ Hence,

• $\large\dashrightarrow$Amount of money Nikhil has as = Rs. 5x

• $\large\dashrightarrow$Amount of money Nikhil has as = Rs. 5x × 60

$\large\dag$ Hence Verified,

• Amount of Nikhil has as Rs. 5 = $\large\underline{\rm{Rs.~300}}$