Question
Aman' and 'Bhuvan' can complete a
certain task in 24 days and 40 days, respectively. Both started working together, but 'Bhuvan' left after 5 days. Afterward, 'Aman' continued working alone until 'Chintu' joined him, and together they completed the task in an additional 5 days. If, instead of 'Chintu,' 'Bhuvan' had rejoined 'Aman' during this second phase of work, it would have taken them 37.5% longer to complete that phase compared to the time taken by 'Aman' and 'Chintu' working together. Quantity-I: Calculate the time 'Chintu' would take to complete the work alone. Quantity-II: Determine the total duration 'Aman' worked. In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Let the total work be 120 units. {LCM (24 and 40) } So, efficiency of 'Aman' = (120/24) = 5 units/day And efficiency of 'Bhuvan' = (120/40) = 3 units/day Let the efficiency of 'Chintu' be 'p' units/day ATQ: (5 + p) × 5 = (5 + 3) × (5 × 1.375) Or, (5 + p) = 8 × 1.375 Or, 5 + p = 11 So, 'p' = 6 Also, efficiency of 'Chintu' = 6 units/day Quantity I: Time taken by 'Chintu' to finish the work alone = (120/6) = 20 days So, Quantity I = 20 days Quantity II: Work done by 'Aman' and 'Bhuvan' in first five days = 5 × (5 + 3) = 40 units And work done by 'Aman' and 'Chintu' in last 5 days = 5 × (5 + 6) = 55 units And work done by 'Aman' alone = 120 - (55 + 40) = 25 units So, 'Aman' worked alone for 25 ÷ 5 = 5 days So, 'Aman' worked for a total of (5 + 5 + 5) = 15 days So, Quantity II = 15 days So, Quantity I > Quantity II
The diagonal of a square is √32 cm. What is the area of the square?
The length of a plot is three times its breadth. A playground measuring 150 square metres occupies half of the total area of the plot. What is the lengt...
If the length of a rectangle is increased by 25% and its breadth is decreased by 8%, then the area of the rectangle will be increased or decreased by ho...
A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 ft, and the sum of the lengths of the...
The sum of the areas of a rectangle and a square is 432 cm². The breadth of the rectangle is 6 cm more than each side of the square. If the length of t...
A hollow spherical metallic ball has an external diameter 6cm and is 1/2cm thick. The volume of the ball (in cm cube) is.
A rectangular park is 50 m long and 30 m wide. A path of uniform width 2 m is built inside the park along all four sides. Find the area of the path.
The radius of the base of a cone is 6 cm, and its slant height is 10 cm. What is the surface area of the cone?
If the area of a square is 400 cm² and the breadth of a rectangle is 20% more and the length is 50% more than the side of the square, then find the rat...
In a triangle ABC, D, E and F are the mid-points of the sides BD, CA and AB, respectively. BE and DF intersect at X. DE and CF intersect at Y. Find XY = ?
