Question

The ratio of 1 rupee, 50 paise and 10 paise coins in a purse is 3: 4: 8, if the total money is 116 in the purse, then give the number of 10 paise.​

Answer 1

GIVEN :

• The ratio of ₹1, 50 paise, and 10 paise in a purse is 3:4:8 respectively.
• The total amount of money is ₹116 in the purse.

TO FIND :

• The number of 10 paise in the purse.

SOLUTION :

• Let's assume that number of :

➡ ₹1 is 3x.

➡ ₹0.50 is 4x.

➡ ₹0.10 is 8x.

Therefore,

Amount of :

➡ ₹1 will be 3x × ₹1 = ₹3x

➡ ₹0.50 will be 4x × ₹0.50 = ₹2x

➡ ₹0.10 will be 8x × ₹0.10 = ₹0.80x.

Now,

• It's being told that total amount of money is ₹116 in the purse.

According to the question,

We can say that,

$\implies \bf \: 3x \: + 2x \: + 0.80x = 116$

$\bf \implies \: 5.80x = 116$

$\bf \implies \frac{580}{100} x = 116$

$\bf \implies x = \frac{\cancel{116} \times 10\cancel0}{\cancel{58} \cancel0}$

$\bold \gray\dag{ \underline{ \boxed{ \green{ \bf \therefore \: x = 20}}}} \bold \gray\dag$

FINALLY,

We get x = 20

HENCE,

No. of ₹1 = 3x = 3 × 20 = 60.

No. of ₹0.50 = 4x = 4 × 20 = 80.

No. of ₹0.10 = 8x = 8 × 20 = 160.$\bold{\bf{\boxed{ \blue{\bf \checkmark }}}} \bf ans.$

${ \underline{ \boxed{ \bf{ \green{ \therefore \: Required \: answer : }}}}}$

$\bold \red\dag{ \underline{ \boxed{ \bf { \orange { \: no. \: of \: 10 \: paise \: is \:8x = 8 \times 20 = 160 \: ans. \blue \checkmark}}}}}$

Verification :

By substituting the value of x in the equation :

$\dashrightarrow \bf \: 3x \: + 2x \: + 0.80x = 116$

$\dashrightarrow \bf \: 3x \: + 2x \: + 0.80x = 116$

$\bf \dashrightarrow \: (3 \times 20) + (2 \times 20) + (0.80 \times 20) = 116$

$\dashrightarrow \bf 60 + 40 + 16 = 116$

$\bf \dashrightarrow \: 116 = 116$

AFTERALL,

L. H. S. = R. H. S.

$\bold \gray \dag{ \underline{\boxed { \green{\bf Hence,\purple V \red e \orange r \pink i \blue f \green i \red e \pink d }}}} \bold \gray \dag$