Let the men leave after x days.

Work done by them in x days = x/40

Remaining work = 1 – x/40

Also, M₁T₁/W₁= M₂T₂/W₂

So, 15×40/1 = 10×(50 – x)/(1 – x/40)

So, 1-x/40 = 10(50 – x)/(15×40)

40 – x = 2(50 – x)/3

120 – 3x = 100 – 2x

X = 20

In 100m race, A = 100m, B = 80m

Between B and C, B = 100m, C = 75m

When B = 80m, C = 60m

So, in a 200m race between A and C, A=200m, C=120m

So, A beats C by 80m

Let distance between the banks be x km

Upstream speed = 4 – 2 = 2km/h; Upstream time = x/2

Downstream speed = 4 + 2 = 6km/h; Downstream time = x/6

Total distance = 2x

Total time = x/2 + x/6 = 2x/3

Average speed for the whole journey = 2x/(2x/3)

= 3km/h

In CI, A=P(1+0.01r)ⁿ

A-Amount, P-Principle/Sum, n- Time period

20000=10000(1+0.01r)³

2 = (1+0.01r)³

Squaring both sides,

4 = (1+0.01r)⁶

Multiplying both sides by 10000,

40000=10000(1+0.01r)⁶

So, the amount will become 40000 in 6 years

5⁵ × 5³ × 2 = 5^2x × 5² × 2

5⁸ = 5^{2x + 2}

Equating exponents, 2x = 6

X = 3

In dia 1, sin w = 7.5√3/15

= √3/2

W = 60°

According to question, in the next wall, the angle of inclination is half

So, w/2 = 30°

If we compare the two triangles, we can see that the second triangle is rotation of the first triangle (If one angle is 30°, the other angle has got to be 60°)

SO, the height of first wall is equal to the distance between foot of ladder and base of building in second case.

So, x = 7.5√3m

√64.05 ≈ 8

∛0.729 ≈ 0.9

So, the given expression becomes

72×7×10/7.2

=700

Let total number of invalid votes be x

Votes for winner = 0.51(8500 - x)

Votes for loser = 0.49(8500 - x)

Difference=0.02(8500-x) = 160

170-0.02x = 160

0.02x = 10

X = 500

2012, let the ages be 3x, 4x

2017, 3x + 5, 4x + 5

(3x + 5)/(4x + 5) = 7/9

27x + 45 = 28x + 35

X = 10

Ages of A and B in 2012 = 30, 40

Ages of A and B in 2022 = 40, 50

Sum = 90

Number of spade cards = 13

Remaining cards=52 – 13 = 39

Number of numbered cards in the remaining three sets = 9 × 3 = 27

Remaining cards = 39 – 27 = 12

So, required Probability = 12/52 = 3/13