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**1.Direction**: There are 40 flats in a society, the water supply (24 hours) to all these flats is provided from a large tank of a capacity of 60000 litres. The tank gets only filled when it becomes fully empty.

In November: 40% of the flats were occupied and each flat uses 25 litres/hr. If the tank was filled at the starting of the month, then the tank should be filled … (A) … times in November.

In December: 50% of the flats were occupied. The tank is filled after every 150 hrs. The rate of use of water per hour by each flat in November is … (B) … percentage more than the rate of use of water per hour by each flat in December.

In January: 50% of the total occupied flats in January consumed 12 litres/hr and the remaining 50% consumed the same amount of water per hour as in December. The tank gets emptied in a total of 125 hrs. In January, … (C) … flats were occupied.

The cost of water charged per litre is Rs. 0.1 per litre. The monthly bill of water for each flat is Rs. 1612.8. If all the flats are occupied in February then the tank will get emptied in each .

**1.Find the value in place of A.**

**A. 4**

**B. 3**

**C. 2**

**D. 5**

**E. 6**

**2.Find the value in place of B.**

**A. 20**

**B. 30**

**C. 25**

**D. 10**

**E. 15**

**3.Find the value in place of C.**

**A. 25**

**B. 32**

**C. 24**

**D. 30**

**E. 20**

**4.Find the value in place of D.**

**A. 75**

**B. 62.5**

**C. 60**

**D. 80**

**E. 57.5**

5.John travels at (x – 20) km/hr, he takes

(y + 5) hours to cover A km. He travels

(x + 10) km/hr, he takes (y – 1) hours to cover A km. He travels at (x – 15) km/hr, he takes

(y + 3) hours to cover A km.

**From the given statement which of the following can be determined?**

A. Value of A.

B. Value of x.

C. Value of y.

D. Find the distance covered by him when he travels at (x + 5) km/hr for (y + 4) hours.

A. Only A and D

B. Only B and C

C. All of them

D. Only A, B and C

E. None

6.Two places are X km apart. Two boats start from each place at the same time towards each other. One is going upstream and another downstream. The speeds of two boats are 12 km/hr and 15 km/hr. Both the boats meet after 4 hours.

**From the given statement which of the following can be determined?**

A. Speed of the current.

B. Value of X.

C. If both the boats travel upstream (Faster boat is behind the slower one) then after how much time will they meet?

D. If both the boats travel downstream (Faster boat is behind the slower one) then after how much time will they meet?

A. Only C and D

B. Only B and C

C. All of them

D. Only A, B and C

E. Only B, C and D

7.Puneet and Vimal invested Rs. A and Rs. B in simple and compound interest respectively. The amount invested by Puneet becomes Rs. 26000 in 3 years and that invested by Vimal becomes Rs. 25920 in 3 years. The difference of rate of interests on the investments by Vimal and Puneet is 10%. Ratio of A and B is 4 : 3.

**From the given statement which of the following can be determined?**

A. Sum of rate of interests on the investments by Vimal and Puneet.

B. Value of A.

C. Value of B.

D. Difference of interest amounts obtained by Vimal and Puneet.

A. Only A and D

B. Only B and C

C. All of them

D. Only A, B and C

E. None

**Direction:( 8 - 12) There**are 5 villages A, B, C, D and E. Each village has a windmill that works on a turbine. Each of these turbines have different capacity to produce the electricity. The mills of villages A, B, C, D and E can produce 1.2L kWh/week, 1L kWh/week , 0.8L kWh/week, 1.5L kWh/week and 2 kWh/week of electricity respectively. Every week the efficiency of the turbine of these windmills changes due to different speed of wind. In 1st week, the efficiencies of the turbines of windmills of villages A, B, C, D and E were 50%, 80%, 60%, 70% and 60%. In 2nd week, the efficiencies of the turbines of the windmills of villages A, B, C, D and E were 90%, 60%, 80%, 70% and 80%. In 3rd week, the efficiencies of the turbines of the windmills of villages A, B, C, D and E were 80%, 60%, 90%, 100% and 80%. In 4th week, the efficiencies of the turbines of the windmills of villages A, B, C, D and E were 100%, 90%, 80%, 80% and 90%. The number of households in each village is 360, 350, 400, 600 and 450 respectively. The produced electricity when transmitted gets wasted in the form of line losses, 25%, 40%, 30%, 20% and 15% of total produced electricity gets wasted in villages A, B, C, D and E respectively. (1 kWh = 1 unit of electricity consumption.) (Electricity Produced = Electricity Consumed + Losses)

**8.If equal amount of electricity is consumed by each household then find per day consumption of electricity by each household in village C in 2nd week.**

**A. 18 units**

**B. 20 units**

**C. 16 units**

**D. 12 units**

**E. 15 units**

**9.What is the difference between the electricity produced by villages B and C together in the 2nd week and the electricity produced by villages A and E together in the 4th week?**

**A. 1.76L kWh**

**B. 1.16L kWh**

**C. 1.24L kWh**

**D. 1.80L kWh**

**E. 1.96L kWh**

**10.Consumption of electricity by each household in village A in 3rd week is how much percentage more than the Consumption of electricity by each household in village D in 4th week?**

**A. 20%**

**B. 30%**

**C. 15%**

**D. 25%**

**E. 18%**

**11.There is variable tariff rate for electricity consumption in village D. Upto 500 units per month, the rate is Rs. 5 per units and beyond that rate is Rs. 6 per unit. Find the amount of bill generated from each house in village D. (1 Month = 4 weeks)**

**A. Rs. 3140**

**B. Rs. 3340**

**C. Rs. 3650**

**D. Rs. 3440**

**E. Rs. 3320**

**12.Find the amount of loss occurred due to wastage of electricity in line losses in village B taking all four week if the cost of production of a unit of electricity is Rs. 2.5.**

**A. Rs. 250000**

**B. Rs. 260000**

**C. Rs. 270000**

**D. Rs. 320000**

**E. Rs. 290000**

__SOLUTIONS:__1.Number of occupied flats in November = 40 × 0.4 = 16

Since each flat uses 25 litres/hr;

∴ Amount of water used in whole month = 16 × 25 × 24 × 30 = 288000 litres

∴ Number of times the tank should be filled = 288000/60000 = 4.8 i.e. 5 times

∴ A = 5

2.In December: 50% of the flats were occupied. The tank is filled after every 150 hrs. The rate of use of water per hour by each flat in November is … (B) … percentage more than the rate of use of water per hour by each flat in December.

In January: 50% of the total occupied flats in January consumed 12 litres/hr and the remaining 50% consumed the same amount of water per hour as in December. The tank gets emptied in a total of 125 hrs. In January, … (C) … flats were occupied.

∴ Required percentage = [25 – 20]/20 = 25%

∴ B = 25

3.In January: 50% of the total occupied flats in January consumed 12 litres/hr and the remaining 50% consumed the same amount of water per hour as in December. The tank gets emptied in a total of 125 hrs. In January, … (C) … flats were occupied.

The cost of water charged per litre is Rs. 0.1 per litre. The monthly bill of water for each flat is Rs. 1612.8. If all the flats are occupied in February then the tank will get emptied in each

⇒ x = 30

∴ C = 30

4.In December: 50% of the flats were occupied. The tank is filled after every 150 hrs. The rate of use of water per hour by each flat in November is … (B) … percentage more than the rate of use of water per hour by each flat in December.

In January: 50% of the total occupied flats in January consumed 12 litres/hr and the remaining 50% consumed the same amount of water per hour as in December. The tank gets emptied in a total of 125 hrs. In January, … (C) … flats were occupied.

∴ Number of hours in which the tank will get emptied = 60000/[40 × 24] = 62.5 hours

∴ D = 62.5

5.According to given statements:

(x – 20) × (y + 5) = A

(xy + 5x – 20y – 100) = A ---- (1)

(x + 10) × (y – 1) = A

(xy – x + 10y – 10) = A ---- (2)

(x – 15) × (y + 3) = A

(xy + 3x – 15y – 45) = A ---- (3)

From equation 1 and 2:

(xy + 5x – 20y – 100) = (xy – x + 10y – 10)

⇒ 6x – 30y = 90 or

⇒ x – 5y = 15 ---- (4)

From equation 1 and 3:

(xy + 5x – 20y – 100) = (xy + 3x – 15y – 45)

⇒ 2x – 5y = 55 ---- (5)

From equation 4 and 5:

⇒ x = 40 and y = 5

Option A: Value of A = (40 – 20) × (5 + 5) = 200 km

Option B: Value of x = 20

Option C: Value of y = 5

Option D:

Distance covered by him when he travels at (x + 5) km/hr for (y + 4) hours = 45 × 9 = 405 km

Hence, we can find all the options.

6.Suppose the speed of the current = ‘s’ km/hr;

The speeds of two boats are 12 km/hr and 15 km/hr;

When the boats travel towards each other, they meet after 4 hours:

⇒ X = (12 + x + 15 – x) × 4

⇒ X = 108 km

When the boats travel in the same direction (Faster boat is behind the slower one):

Suppose both the boats are moving upstream:

∴ Time after which the boats will meet = 108/[(15 – x) – (12 – x)] = 108/3 = 36 hours

Suppose both the boats are moving downstream:

∴ Time after which the boats will meet = 108/[(15 + x) – (12 + x)] = 108/3 = 36 hours

Speed of the current can’t be determined.

∴ Only B, C and D can be determined.

7.Suppose ‘R’ and ‘r’ are the rate of interest on investments by Vimal and Puneet;

According to the given data:

26000 = A + [A × r × 3]/100

⇒ A × [1 + 3r/100] = 26000 ---- (1)

And

25920 = B × [1 + R/100]3 ---- (2)

Dividing both the equations:

Given that A : B = 4 : 3 and

R – r = 10

If we put these values in the equation, we can get the values of R and r;

If we get the rate of interest, we can calculate the investments A & B too.

After getting the investments, we can also get the difference of interest amount.

∴ All the values can be determined.

8.Amount of electricity produced by windmill in village C in 2nd week = 0.8 × 0.8 = 0.64L kWh

Since 30% of the produced electricity is wasted due to line losses.

⇒ Amount of electricity used for consumption = 0.64 × 0.7 = 0.448L kWh = 44800 kWh

Since there are 400 households in village C.

∴ Per day consumption of electricity by each household = 44800/ (400 × 7) = 16 kWh = 16 units

9.Electricity produced by villages B and C together in 2nd week = 1 × 0.6 + 0.8 × 0.8 = 1.24L kWh

Electricity produced by villages A and E together in 4th week = 1.2 × 1 + 2 × 0.9 = 3L kWh

∴ Required difference = 3 – 1.24 = 1.76L kWh

10.Amount of electricity produced by windmill in village A in 3rd week = 1.2 × 0.8 = 0.96L kWh

Since 25% of the produced electricity is wasted due to line losses

⇒ Amount of electricity used for consumption = 0.96 × 0.75 = 0.72L kWh = 72000 kWh

Since there are 360 households in village A

⇒ Consumption of electricity by each household in village A in 3rd week = 72000/360 = 200 kWh = 200 units

Amount of electricity produced by windmill in village D in 4th week = 1.5 × 0.8 = 1.2L kWh

Since 20% of the produced electricity is wasted due to line losses

⇒ Amount of electricity used for consumption = 1.2 × 0.8 = 0.96L kWh = 96000 kWh

Since there are 600 households in village D

⇒ Consumption of electricity by each household in village D in 4th week = 96000/600 = 160 kWh = 160 units

∴ Required percentage = [200 – 160] /160 = 25%

11.Total electricity produced in village D in 4 weeks = 1.5 × (0.7 + 0.7 + 1.0 + 0.8) = 4.80L kWh

Since 20% of the produced electricity is wasted due to line losses

⇒ Amount of electricity used for consumption = 4.80 × 0.8 = 3.84L kWh

Since there are 600 households in village D

⇒ Per month consumption of electricity by each household = 384000/(600) = 640 kWh = 640 units

Upto 500 units per month, the rate is Rs. 5 per units and beyond that rate is Rs. 6 per unit.

∴ Amount of bill generated from each house = 500 × 5 + 140 × 6 = Rs. 3340

12.Total electricity produced in village B in 4 weeks = 1 × (0.8 + 0.6 + 0.6 + 0.9) = 2.9L kWh

Since 40% of the produced electricity is wasted due to line losses.

⇒ Amount of electricity wasted = 2.9 × 0.4 = 1.16L kWh

∴ Amount of loss occurred due to wastage of electricity = 1.16 × 100000 × 2.5 = Rs. 290000

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