Question

Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditure are in the ratio 4:3. If each of them saves Rs. 50 at the end of the month, find their pocket money.

Answer 1

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Let the income of Zahira and Zohra be Rs 6x and Rs 5x respectively.

And let the expenditure of Zahira and Zohra be Rs 4y and Rs 3y respectively.

Then savings of Zahira and Zohra are Rs (6x – 4y) and Rs (5x – 3y) respectively.

According to question,

6x – 4y=50

⇒3x−2y=25

⇒15x−10y=125 ------(1)

and 5x−3y=50

⇒15x−9y=150 ------(2)

Subract (1) from (2), we get

−9y−(−10y)=150−125

⇒y=25

Put the value of y in (1) we get

15x−10(25)=125

⇒15x=125+250

⇒15x=375

⇒x=25

So, income of Zahira=6×x=6×25=Rs150

and income of Zohra=5×x=5×25=Rs125

Answer 2

Answer:

Let the income of Zahira and Zohra be Rs 6x and Rs 5x respectively.

And let the expenditure of Zahira and Zohra be Rs 4y and Rs 3y respectively.

Then savings of Zahira and Zohra are Rs (6x – 4y) and Rs (5x – 3y) respectively.

According to question,

6x – 4y=50

⇒3x−2y=25

⇒15x−10y=125 ------(1)

and 5x−3y=50

⇒15x−9y=150 ------(2)

Subract (1) from (2), we get

−9y−(−10y)=150−125

⇒y=25

Put the value of y in (1) we get

15x−10(25)=125

⇒15x=125+250

⇒15x=375

⇒x=25

So, income of Zahira=6×x=6×25=Rs150

and income of Zohra=5×x=5×25=Rs125