UPSC CDS 2 2021 Math Paper

Let cost of chair be x and cost of table be y.
Then, x+y=750 ... (i)
By selling the chair at a gain of 5% and the table at a gain of 20%, there is a profit of 16% on the whole.

Then, (x+5% of x)+(y+20% of y) =750+(16% of 750)
⇒(x+‌

5

100

×x)+(y+‌

20

100

×y) =750+‌

16

100

×750
⇒100x+5x+100y+20y
=75000+12000
⇒105x+120y=87000
From Eq. (i), put y=750−x into Eq. (ii), we get
⇒105x+120(750−x)=87000
⇒105x+90000−120x=87000
⇒90000−87000=120x−105x
⇒3000=15x
⇒‌‌x=200
∴‌‌y=750−200‌‌ [from Eq. (i)] ‌‌=550
Hence, the original cost of the table is ₹ 550 .