Question

hey mate can u answer the following question

Answer 1

Amount given by Rishi's mother =Rs 245 in the form of 10 rupees, 5 rupees and 15 rupees cards

Let her have ‘x’ 10 rupees cards.

Then given that

5 rupees cards =\frac {2}{3} x=

3

2

x and

15 rupees cards =\frac{1}{5} x=

5

1

x

Total amount

\begin{lgathered}\begin{array} { c } { = 10 x + 5 \times \frac { 2 } { 3 } x + 15 \times \frac { 1 } { 5 } x } \\\\ { = 10 x + \frac { 10 x } { 3 } + 3 x } \\\\ { = 13 x + \frac { 10 x } { 3 } = \frac { 39 x + 10 x } { 3 } } \\\\ { = \frac { 49 x } { 3 } } \end{array}\end{lgathered}

=10x+5×

3

2

x+15×

5

1

x

=10x+

3

10x

+3x

=13x+

3

10x

=

3

39x+10x

=

3

49x

The two amounts must be equal so :

\begin{lgathered}\begin{array} { c } { \frac { 49 x } { 3 } = 245 } \\\\ { 49 x = 245 \times 3 } \\\\ { x = \frac { 245 \times 3 } { 49 } = 5 \times 3 } \\\\ { x = 15 } \end{array}\end{lgathered}

3

49x

=245

49x=245×3

x=

49

245×3

=5×3

x=15

Thus,

10 rupees cards x = 15

5 rupees cards = \frac {2}{3}\times15=10=

3

2

×15=10

15 rupees cards =\frac {1}{5}\times15=3=

5

1

×15=3

So, she has 15 ten rupees cards , 10 five rupees cards and 3 fifteen rupees cards.