SSC CGL (Combined Graduate Level) Quantitative Aptitude Syllabus

If a value is increased by x% and then decreased by x%, what is the net percentage change?

There is a net decrease of x^2/100 percent. (Successive +x% then -x% gives -x^2/100 %, never zero.)

What is the formula for net effect of two successive percentage changes a% and b%?

Net % change = a + b + (ab/100), using positive signs for increase and negative for decrease.

Express the common fractions for 12.5%, 16.66%, 33.33%, and 66.66%.

12.5% = 1/8; 16.66% = 1/6; 33.33% = 1/3; 66.66% = 2/3.

What are the formulas for Profit, Loss, Profit% and Loss% in terms of Cost Price (CP) and Selling Price (SP)?

Profit = SP - CP; Loss = CP - SP. Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Profit/Loss percent is always calculated on CP.

How do you find SP from CP given a profit% or loss%?

SP = CP x (100 + Profit%)/100, or SP = CP x (100 - Loss%)/100.

What is Marked Price (MP), and how does Discount relate to it?

Marked Price is the listed/tag price before discount. Discount = MP - SP, and Discount% = (Discount/MP) x 100. SP = MP x (100 - Discount%)/100.

What is the formula for the net effect of two successive discounts of x% and y%?

Equivalent single discount = x + y - (xy/100) percent.

When goods are sold at the same price, one at x% profit and another at x% loss, what is the overall result?

There is always an overall loss of (x^2/100) percent (loss = (common gain/loss%)^2 / 100).

What is the formula for Simple Interest (SI), and for the Amount?

SI = (P x R x T)/100, where P = principal, R = rate% per annum, T = time in years. Amount = P + SI.

What is the formula for Compound Interest (CI) compounded annually?

Amount = P(1 + R/100)^T, and CI = Amount - P = P[(1 + R/100)^T - 1].

How is the compound interest formula adjusted for half-yearly and quarterly compounding?

Half-yearly: A = P(1 + (R/2)/100)^(2T). Quarterly: A = P(1 + (R/4)/100)^(4T). The rate is divided and time multiplied by the number of compounding periods per year.

For the same P, R, and T = 2 years, what is the difference between CI and SI?

Difference = P x (R/100)^2 for 2 years. For 3 years, Difference = P x (R/100)^2 x (3 + R/100).

At what rate of simple interest does a sum double, and how does this compare to compound interest doubling?

Under SI, a sum doubles when total interest equals the principal: T = 100/R years. Under CI, the time to double is found from 2 = (1 + R/100)^T (approximately 72/R years by the Rule of 72).

In partnership, how are profits shared among partners?

Profit is shared in the ratio of each partner's capital multiplied by the time it was invested (Capital x Time).

Distinguish a simple partnership from a compound partnership.

In a simple partnership, all partners invest for the same time, so profit is shared in the ratio of capitals. In a compound partnership, capitals are invested for different times, so profit is shared in the ratio of (Capital x Time) for each partner.

What is the difference between a working (active) partner and a sleeping (dormant) partner?

A working partner manages the business and may receive a salary/commission in addition to a profit share; a sleeping partner only invests capital and shares profit without managing the business.

What is the basic relationship between Speed, Distance, and Time?

Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

How do you convert km/hr to m/s and m/s to km/hr?

km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

For two trains/objects moving, what are the relative speeds in the same and opposite directions?

Same direction: relative speed = difference of speeds. Opposite directions: relative speed = sum of speeds.

How long does a train of length L take to cross a pole and to cross a platform of length P?

Crossing a pole/man: time = L / speed. Crossing a platform/bridge of length P: time = (L + P) / speed.

In boats and streams, what are the downstream and upstream speeds in terms of boat speed b and stream speed s?

Downstream speed = b + s; Upstream speed = b - s. Hence b = (downstream + upstream)/2 and s = (downstream - upstream)/2.

If A can do a piece of work in n days, what is A's one-day work, and how is combined work found?

A's one-day work = 1/n. If A does work in a days and B in b days, together they do (1/a + 1/b) per day, finishing in ab/(a+b) days.

State the work-rate relationship using the concept of total work (LCM method).

Take total work = LCM of the individual times. Each worker's efficiency (units/day) = Total work / their time. Combined time = Total work / sum of efficiencies.

What is the inverse relationship between the number of workers (or efficiency) and time to complete a fixed work?

For a fixed amount of work, time is inversely proportional to the number of workers/efficiency: more workers means proportionally less time (M1 x D1 = M2 x D2).

State the work formula relating men (M), days (D), hours (H), and work (W) for two situations.

(M1 x D1 x H1) / W1 = (M2 x D2 x H2) / W2. This equates the work-per-effort across two scenarios.

State the algebraic identities for (a+b)^2, (a-b)^2, and a^2 - b^2.

(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; a^2 - b^2 = (a+b)(a-b).

State the identities for (a+b)^3, (a-b)^3, and a^3 + b^3, a^3 - b^3.

(a+b)^3 = a^3 + b^3 + 3ab(a+b); (a-b)^3 = a^3 - b^3 - 3ab(a-b); a^3 + b^3 = (a+b)(a^2 - ab + b^2); a^3 - b^3 = (a-b)(a^2 + ab + b^2).

State the identity for a^3 + b^3 + c^3 - 3abc.

a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca). If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.

What are the methods to solve a pair of linear equations in two variables?

Substitution, elimination, cross-multiplication (algebraic methods), and the graphical method (intersection of two lines).

For two linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, what conditions give a unique solution, no solution, or infinitely many solutions?

Unique solution (intersecting lines): a1/a2 != b1/b2. No solution (parallel lines): a1/a2 = b1/b2 != c1/c2. Infinitely many solutions (coincident lines): a1/a2 = b1/b2 = c1/c2.