# Solution

1. 3;
Sum of the weight of A, B, C and D = 75 × 4 = 300 kg

and average weight of A, B, C, D and E = 71 kg

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sum of the weight of A, B, C, D and E

= 71 × 5 = 355 kg

weight of E = 355 – 300 = 55 kg

weight of F = 55 + 6 = 61 kg

Now, average weight of F, B, C, D and E = 72 kg

Sum of the weight of F, B, C, D and E = 72 × 5 = 360 kg

B + C + D = 360 – 55 – 61 = 244 kg.

Weight of A = 300 – 244 = 56 kg.

2. 1;
Let the marked price be Rs. 100 and the cost price be Rs. x

(84 – x)/x * 100 = 20

x = Rs. 70

Gain% = (80 – 70)/70 * 100 = 14 2/7%

3. 2;
Now, milkman sold 40 litre of mixture

So, remaining mixture = 165 – 40 = 125 litre

Quantity of water = 125 × 28/100 = 35 litre

Quantity of milk = 90 litre.

Now, milkman made new mixture in which

water = 35 + 13 = 48 litre

milk = 90 + 30 = 120 litre

Percentage of water in the new mixture

= 48/(48 + 120) * 100 = 28.57%

4. 4;
Let the breadth of the rectangle plot be x m.

Given, width of the path = 4 m

Area of the path = 432 m^2

and length of rectangular plot = (x + 2) m

2 × [4x (x + 2) + 4x – 2 × 4 × 4] = 432 m^2

8 (x + 2 + x – 8) = 432 m2

8 (2x – 6) = 432

16 (x – 3) = 432 Þ x = 30 m

Area of plot = x × (x + 2) = 30 × 32 = 960 m^2

5. 4;
Difference of CI and SI in 2 years = Pr^2/(100)^2

r^2 = 15%

6. 5;
12 men × 36 days = 18 women × 60 days

2m = 5w

8m = 20w

(8m + 20w) × 20 days + xw × 4 days = 18w × 60 days

40 × 20 + x × 4 = 18 × 60 Þ 4x = 1080 – 800

x = 280/4

= 70 women

7. 5;
Total number of ways

= 5C1 × 4C2 + 5C2 × 4C1 +5C3

5 × 4*3/2 + 5*4/2 + 5*4*3/3*2

= 30 + 40 + 10 = 80 ways

8. 1;
Let distance be LCM of speeds = 192 km

Time taken by bus without stoppage = 192/64 = 3hr

Time taken by bus with stoppage = 192/48 = 4hr

Bus stops in 4 hours for 60 min

Bus stops in 1 hr for 60/4

= 15 min

9.4;
Required Probability = 3C2/9C2 = 1/12

10.3
Let the investment by Rahul be x

Mohit = x * 90/100 = 9x/10

Pradeep = 9x/10 * 120/100 = 108x/100

x + 9x/10 + 108x/100 = 17880

x = Rs. 6000