UPSC CDS 1 2022 Math Paper

Given:
Marked Price of article = Rs. 200
Discount =10% on Marked Price
Gain =20% on Cost Price
Concept Used:
‌ S.P ‌=‌ M.P ‌[100−D%]%
‌ S.P ‌=‌ C.P ‌[100+P%]%
Where, S.P = Selling Price
M.P = Marked Price, C.P = Cost Price
D%=
Discount Percent, P%= Profit Percent
Calculation:
Let the cost price of article be Rs. x
‌ S.P ‌=‌ M.P ‌[100−D%]%
⇒S.P=200×[100−10]%
⇒S.P=200×90∕100=‌ Rs. ‌180‌‌−−(i)
Now, S.P = C.P [100+P%]%
⇒S.P=x×[100+20]%
⇒S.P=x×(120∕100)
⇒S.P=6x∕5‌‌⋯ (ii)
Now, From (i) and (ii), we get
6x∕5=180
⇒x=150
∴ The cost price of article is Rs. 150 .