Golden rule: the base is always the original quantity.
Fraction → percentage: multiply by 100. Percentage → fraction: divide by 100.
Successive change of a% then b% → net =a+b+100ab (use negative signs for decreases).
Product constancy: if price rises x%, consumption must fall by 100+xx×100% to keep spend fixed.
2. Profit, Loss & Discount
Profit / loss is always on Cost Price (CP) unless stated otherwise.
Profit %=CPSP−CP×SP=CP(100100±P/L%)
Discount is on Marked Price (MP): Discount%=MPMP−SP×100.
Markup is on CP: .
CPMP=100−Discount%
3. Simple & Compound Interest
SI=100PRTA=
CI − SI over 2 years:P(100R)2
CI − SI over 3 years:
1.
A software engineer has a target package of Rs. 30,00,000 per annum. Upon receiving it, he invests 20% of his salary in mutual funds, 15% of the remaining amount in fitness equipment, and 30% of the further remaining amount on rent and living expenses. If he saves the rest, what is his annual savings?
2.
In an election for a college tech council, Candidate A received 45% of the total valid votes. 20% of the total votes polled were declared invalid. If the total number of votes polled was 15,000, find the number of valid votes secured by Candidate B (assuming there are only two candidates).
3.
The monthly subscription price of a MERN stack development course was decreased by 25%, which led to a 40% increase in the number of students enrolling. Find the net percentage increase or decrease in the total revenue.
4.
A developer launches a new SaaS platform called Codify. He marks the subscription price 40% above the actual cost of hosting and maintenance. If he offers a discount of 15% to his early-bird users, what is his actual profit percentage?
5.
A manufacturer sells a laptop to a wholesaler at a profit of 20%. The wholesaler sells it to a retailer at a profit of 25%, and the retailer sells it to a customer for Rs. 54,000, earning a profit of 20%. What was the original manufacturing cost of the laptop?
6.
A merchant mixes 20 kg of premium whey protein bought at Rs. 1200 per kg with 30 kg of standard whey protein bought at Rs. 1500 per kg. At what price per kg should he sell the final mixture to gain an overall profit of 20%?
100
Loss %
=
CPCP−SP×
100
C
P
=
SP(100±P/L%100)
Markup%=CPMP−CP×100
MP/CP master relation (given both discount and profit):
100
+
Profit%
P
(1+100R)n
,
C
I
=
A−
P
P(100R)2(3+100R)
Rule of 72: money doubles in roughly 72/R years at rate R% compounded.
7.
The difference between the compound interest (compounded annually) and the simple interest on a certain sum of money for 2 years at 8% per annum is Rs. 128. Find the principal sum.
8.
What will be the compound interest on a sum of Rs. 16,000 for 1.5 years at 10% per annum, if the interest is compounded half-yearly?
9.
A sum of money placed at simple interest triples itself in 8 years. In how many years will it become 5 times of itself at the exact same rate of interest?
10.
A man borrowed Rs. 21,000 at 10% per annum compound interest. If the debt is to be completely discharged in two equal annual installments, what is the value of each installment?