Question

Dhara has a total of Rs 9100 as currency notes in the denominations of Rs 500, Rs200 and Rs 100. The ratio of the number of Rs 500 notes to Rs 100 notes is 4:5. If she has a total of 35 notes, how many notes of each denomination does she have ?​

Answer 1

✰ Question :-

Dhara has a total of Rs 9100 as currency notes in the denominations of Rs 500, Rs200 and Rs 100. The ratio of the number of Rs 500 notes to Rs 100 notes is 4:5. If she has a total of 35 notes, how many notes of each denomination does she have ?

✪ Solution :-

It is given that dhara has Rs.500 and Rs.100 notes in ratio 4:5.

Lets say that, she as 4x notes of Rs.500 and 5x notes of Rs.100 .

Now, it is given that, she total has 35 notes .

So, Notes of Rs.200 left = (35 - 4x - 5x) = (35-9x) Notes .

Now, it is given that, she Total has Rs.9100 as currency .

So,

⟼ 100*5x + 200(35-9x) + 500*4x = 9100

⟼ 500x + 7000 - 1800x + 2000x = 9100

⟼ 500x + 200x = 9100 - 7000

⟼ 700x = 2100

Dividing both sides by 700, we get,

⟼ x = 3

So,

☛ Notes of Rs.500 , she has = 4x = 4*3 = 12 Notes .

☛ Notes of Rs.100 she has = 5x = 5*3 = 15 notes .

☛ Notes of Rs.200 she has = (35 - 12 - 15) = 8 notes .

Hence, Dhara has 15 notes of Rs.100 , 8 notes of Rs.200 and 12 notes of Rs.500.

Answer 2

Answer:

$\bf\red{Solution:-}$

$\bf\red{Here}\begin{cases}\sf\green{Total\:currency = Rs.9100}\\\sf\red{Denominations:Rs.500,Rs.200,Rs.100}\\\sf\purple{Rs.500 : Rs.100 = 4 : 5}\\\sf\orange{Total\:notes = 35}\\\sf\red{Number\:of\:each\:denominations=?}\end{cases}$

Let denominations of Rs.500 be 4x and Rs.100 be 5x.

→ Denominations of Rs.200 = Total notes - (Denominations of Rs.500 + Dm.of Rs.100)

→ Denominations of Rs.200 = 35 - (4x + 5x)

→ Denominations of Rs.200 = (35 - 9x)

${\underline{\underline{\bold{According\:to\:question:-}}}}$

$\hookrightarrow\sf [500 \times 4x + 100 \times 5x + 200 \times (35 - 9x)] = 9100 \\\\\hookrightarrow\sf [2000x + 500x + 7000 - 1800x] = 9100 \\\\\hookrightarrow\sf 2500x - 1800x + 7000 = 9100 \\\\\hookrightarrow\sf 700x = 9100 - 7000 \\\\\hookrightarrow\sf 700x = 2100 \\\\\hookrightarrow\sf x =\cancel{\dfrac{2100}{700}} \\\\\hookrightarrow\huge{\boxed{\sf\purple{x = 3}}}$

$\rule{300}{1}$

•Number of denominations:-

→ Number of Rs.500 = 4x = 4×3 =$\huge{\boxed{\bold\red{12}}}$

→Number of Rs.200 = 35-9x =35 -9 × 3=$\huge{\boxed{\bold\orange{8}}}$

→ Number of Rs.100 = 5x = 5 × 3 =$\huge{\boxed{\bold\green{15}}}$