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A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?
A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is
Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi's total monthly savings (in Rs) is
A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is
Total travel time gets reduced by 75%. So, total travel time becomes 1/4th of the original.
So, s’(New speed) = 4s(Original speed)
Speed of boat : Speed of river = x:1
When the speed of boat is normal
Speed Upstream = x-1
Speed Downstream = x+1
Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/ (a+b)
Here, average speed will be 2(x^2-1)/2x = (x^2-1)/x
When the speed of boat is doubled
Speed upstream = 2x-1
Speed downstream = 2x+1
Here, the distance is constant. So, average speed can be found out by the harmonic mean of two speeds = 2ab/(a+b)
Here, average speed will be 2(4x^2-1)/4x = (4x^2-1)/2x
Now, we know that
New speed = 4*Original speed
(4x^2-1)/2x = 4(x^2-1)/x
4x^2 – 1 = 8x^2 – 8
4x^2 = 7
x = √7/2
Ratio = x:1 = √7/2
Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9: 10: 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is
A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7: 17: 16 for popcorn and 6: 15: 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio
In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is
If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?
A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is
Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC.If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is
A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1: 1: 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is cubic centimeters. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
If x = 40 then y + z = 15. Now since both y and z are natural numbers less than 12, so y can range from 3 to 12 giving us a total of 10 solutions. Similarly, if x = 39, then y + z = 14. Now y can range from 2 to 12 giving us a total of 11 solutions.
If x = 38, then y + z = 13. Now y can range from 1 to 12 giving us a total of 12 solutions.
If x = 37 then y + z = 12 which will give 11 solutions.
Similarly on proceeding in the same manner the number of solutions will be 10, 9, 8, 7 and so on till 1.
Hence, required number of solutions will be (1 + 2 + 3 + 4 . . . . + 12) + 10 + 11
For the value of given expression to be minimum, the values of and should be as close as possible. 30/4 = 7.5. Since each one of these are integers so values must be 8, 8, 7, 7. On putting these values in the given expression, we get
Total ways of distributing 7 things among 4 people so that each one gets at least one = n-1Cr-1 = 6C3 = 20 Now we need to subtract the cases where any one person got more than 3 erasers. Any person cannot get more than 4 erasers since each child has to get at least 1. Any of the 4 childs can get 4 erasers. Thus, there are 4 cases. On subtracting these cases from the total cases we get the required answer. Hence, the required value is 20 - 4 = 16
a1= 3 and a2= 7. Hence, the common difference of the AP is 4.
We have been given that the sum up to 3n terms of this AP is 1830.
Hence, 1830 = m/2 [2*3 + (m – 1) *4]
=> 1830*2 = m(6 + 4m - 4)
=> 3660 = 2m + 4m2
=> 2m2 + m -1830 = 0
=> (m - 30)(2m + 61) = 0
=> m = 30 or m = -61/2
Since m is the number of terms so m cannot be negative. Hence, must be 30
So, 3n = 30
n = 10
Sum of the first '10' terms of the given AP = 5*(6 + 9*4) = 42*5 = 210
m(a1 +a2 +...+an) > 1830
=> 210m > 1830
=> m > 8.71
Hence, smallest integral value of 'm' is 9.
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