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andsy's version from 2018-06-18 10:59

Section 1

Question Answer
If A working Alone takes a days more than A & B, & B working Alone takes b days more than A & B. Then , Number of days, taken by A & B working together to finish a job is = √ab
If A & B working together can finish a work in x days & B is k times efficient than A, then the time taken by, A working Alone will take ⇒ (k + 1) x
If A & B working together can finish a work in x days & B is k times efficient than A, then the time taken by B working Alone will take ⇒ ((k+1)/k)x
If A can finish a work in x days and B is k times efficient than A, then the time taken by both A and B, working together to complete the work is x/(1+k)
If A & B working together, can finish a piece of work is x days, B & C in 4 days, C & A in z days. Then, A + B + C working together will finish the job is ⇒2xyz/(xy+yz+zx)
Two persons A & B, working together, can complete a piece of work in x days. If A, working alone, can complete the work in y days, then B, working alone, will complete the work in ⇒xy/(y-x)
If A, B & C will working alone, can complete a work in x, y and z days, respectively, then they will together complete the work in xyz/(xy+yz+zx)
If A can do a piece of work is x days and B can do a piece of work in 4 days, then both of them working together will do the same work in xy/(x+y) days
If working efficiency of A & B is → x:y. Then, the time taken by A & B to finish the work is in the ratio → y:x

Section 2



Question Answer
Lateral surface Area(पार्श्व पृष्ठ का क्षेत्रफल ) = Perimeter of Base × Height Base = 2(l + b) × h
Total surface area (कुल पृष्ठ का क्षेत्रफल )= Lateral surface Area + 2 × Area of base = 2 (lh + bh + lb)
Diagonal (विकर्ण)= √(l²+b²+h² )
Total surface area(advance)= (sum of all three side)² – (Diagonal)²
Volume of the cube (घन का आयतन)=(√(total surface area)/6)³
In Radius of cube(घन की अन्तः त्रिज्या)=a/2
Circumradius of cube(घन की परित्रिज्या) =√3/2 a

Section 3

Right circular cone
Question Answer
Volume (वक्र पृष्ठ का क्षेत्रफल)= 1/3×area of base×height = 1/3 πr² h
Curved surface area(कुल पृष्ठ का क्षेत्रफल)= 1/2 (Perimeter of base) × slant height = 1/2 × 2πr×l=πrl=πr√(r²+h² )
Total surface area(कुल पृष्ठ का क्षेत्रफल) = C.S.A + Area of base = πrl+πr²=πr(l+r)
Radius of maximum size sphere in a cone(एक शंकु के भीतर अधिकतम आकार के गोले की त्रिज्या) (h × r)/(l + r)
If cone is cut parallel to its base and ratio of heights, radius or slant height of both parts is given as →x∶y Then Ratio of their volume x³ ∶y³
Volume of pyramid1/3 (Area of base) × height
Lateral Surface area 1/2 (Perimeter of base) × Slant height.
Average of n natural no's=(n+1)/2
Average of even No'=(n+1)
Average of odd No'= n


Question Answer
Suppose A invests Rs. x for p months and B invests Rs. y for q months then,(A's share of profit):(B's share of profit)= xp:yq
Let a container contains x units of liquid from which y units are taken out and replaced by water.The quantity of pure liquid after 'n' operations is equal to[ x ( 1 - y/x}^n]
Gain% {(Gain*100)/C.P.}
S.P. = {(100+Gain%) / 100} * C.P.
C.P. = {(100 / (100+Gain%)} * S.P.
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given {x^2/100}%
A single discount equivalent to discount series of x% and y% given by the seller is equal to {x +y - xy/100}%
If a trader professes to sell his goods at cost price, but uses false weights, then Gain% {Error/(True value - Error) x 100}%


Question Answer
If distance travelled for each part of the journey, ie d1=d2=d3=...=dn=d, then average speed of the object is Harmonic Mean of speeds. 2xy/(x + y)
If time taken to travel each part of the journey, ie t1=t2=t3=…tn=t, then average speed of the object is Arithmetic Mean of speeds


Question Answer
Two persons A and B start at the same time from two points P and Q .They meet at a point R and A takes ta time to reach Q and B takes tb time to reach P. speed Sa/Sb & T to reach at R−−−√tb/ta & Thus −−−√ta*tb