SKILLWILL: September 2024

HCF and LCM

If Remainder same:

HCF(n1-R, n2-R, n3-R)

LCM(n1,n2,n3) - R

If Remainder is Different:

HCF(n1-r1, n2-r2, n3-r3)

LCM(n1, n2, n3)-(n1-r1) if n1-r1 = n2-r2 = n3-r3

Surface area and Volumes

Cube

Lateral surface area: 4a**2

Total surface area: 6a**2

Volume: a**3

Cuboid

Lateral surface area: 2(l+b)h

Total surface area: 2(lb+bh+hl)

Volume: l*b*h

Cylinder

Curved Surface area: 2*pi*r*h

Total surface area: 2*pi*r(r+h)

Volume: pi*r**2*h

Cone:

Lateral surface area: pi*r*l

Total surface area: pi*r(r+l)

Volume: 1/3*pi*r**2*h

Sphere:

Surface area: 4*pi*r**2*h

Volume: 4/3*pi*r**2*h

Simple Interest

1. Difference between simple interest & compound interest for 2 years = pr**2/100**2

2. Same for 3 years = pr**2(300+r)/100**3

3. Compound Interest > Simple Interest

4. Simple Interest = PTR/100

5. Amount = Principle + interest

6. Compound Interest = P(1+r/100)**n - p

Work and Time

Work and Time Apptitude Questions

Trick 1: If M1 men can finish W1 work in D1 days and M2 men can finish W2 work in D2 days then, the relation is: M1*D1/W1 = M2*D2/W2

Trick 2: If M1 men finish W1 work in D1 days, working T1 time each day and M2 men finish W2 work in D2 days, working T2 time each day, then the relation is: M1*D1*T1/W1 = M2*D2*T2/W2

Trick 3: If A completes a piece of work in ‘x’ days, and B completes the same work in ‘y’ days, then,

Work done by A in 1 day = 1/X

Work done by B in 1 day = 1/Y

Work done by A and B in 1 day = 1/X + 1/Y

Total time taken to complete the work by A and B both = XY/(X + Y)

Trick 4: If A can do a work in ‘x’ days, B can do the same work in ‘y’ days, C can do the same work in ‘z’ days, then the total time taken by A, B and C to complete the work together = XYZ/(XY + YZ + ZX)

Trick 5: If A alone can do a certain work in ‘x’ days and A and B together can do the same work in ‘y’ days, then B alone can do the same work in = XY/(X – Y)

Trick 7: If A can do a work in ‘x’ days and B can do the same work in ‘y’ days and when they started working together, B left the work ‘m’ days before completion then the total time taken to complete work is = (Y + M)X / (X+Y)

Trick 8: If A leaves the work ‘m’ days before its completion then the total time taken to complete work is = (X + M)Y / (X+Y)