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Two individuals, A and B, have rented a field. A places 21 horses in the field for 6 months and 15 cows for 2 months. B adds 15 cows for 6 months and 40 sheep for 7.5 months. If 3 horses consume the same amount of food as 5 cows, and 6 cows eat as much as 10 sheep, what portion of the rent should A cover?
The investments of three partners, P, Q, and R, are initially in the ratio 6 : 7 : 9. After a year, P adds ₹30,000, Q adds ₹25,000, and R adds some amount to their respective investments. The new ratio of their investments becomes 8 : 9 : 11. Find the amount (in ₹) added by partner R.
A ₹36,000 annual bonus is distributed among Sales, Marketing, and Operations in a 4:5:3 ratio. Marketing uses ₹3,000 for team building and ₹1,500 for an intern, then allocates the rest to two top performers in a 5:4 ratio. How much does the top performer with the smaller share receive?
A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%, B decreases his capital by 1/3, and C leaves the capital unchanged. At the end of the year, if the total profit is Rs. 33,000, find the share of B. (SSC CGL MAINS 19 JAN 2026)
If a : b = 3 : 4 and b : c = 5 : 7, find a : b : c.
Find the mean proportional between 9 and 4.
Find the third proportional to 18 and 36.
Find the fourth proportional to 12, 16, 18.
Find the average of the numbers: 49, 57, 51, 48, 59.
Find the Simple Interest when Principal = 10000, Rate = 8% per annum, and Time = 5 years.
The price of petrol shot up by 5%. Before the hike, the price was Rs. 2 per litre. A man travels 3045 km every month and his car gives a mileage of 15 km per litre. What is the increase in the monthly expenditure (to the nearest Rs.) on the man’s travel due to the hike in the petrol prices?
A landlord bought a flat for 800,000. He wants to earn a 9% annual return on his investment after paying 2,000 per month for maintenance. What should be the monthly rent he charge?
A’s salary is 40% more than B’s. If B’s salary increases by 20% and A’s increases by x%, then A’s new salary becomes 25% more than B’s new salary. What is the value of x?
The production of bottles rose to 26000 from 16000 in 2 years. Find the rate of growth per annum.
The price of a product is decreased by x% and then increased by x%. The final price becomes 10% less than the original. What is the value of x (approximately)?
Find the value of 3¹ + 3² + 3³ + … + 3⁸.
How many integers in the set {1, 2, 3, …, 100} have exactly 3 divisors?
The diagonals of three faces of a rectangular parallelepiped that meet at a single corner measure √5 cm, √10 cm, and √13 cm. What is the volume of this parallelepiped?
In an equilateral triangle the circumcenter coincide with which of the following?
The following table shows marks obtained by students out of 50. Determine the median.Class Interval (Marks) : Frequency0-10 : 510-20 : 820-30 : 630-40 : 640-50 : 5
A rectangle has area 48 cm² and perimeter 28 cm. If the midpoints of the sides are joined to form a rhombus, what is the area of the rhombus?
In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?
In a right-angled triangle ABC, ∠B = 90°. If AB = 6 cm and BC = 8 cm, what is the distance between the centroid (G) and the orthocenter (H)?
In a triangle △PQR, ∠R = 62°. The perpendicular bisector of PQ at S meets QR at T. If ∠TPR = 38°, what is the measure of ∠PQR?
What is the value of 3 − (sin 239° + sin 251°)?
If (sinθ)/x = (cosθ)/y, prove that sinθ − cosθ = (x − y)/√(x² + y²).
Simplify the trigonometric expression (tan²θ − sin²θ) / (2 + tan²θ + cot²θ).
P and Q can do a work in 20 and 30 days respectively. They work together for 6 days, then Q is replaced by R. Remaining work is completed in 8 days. In how many days can R alone complete 60% of the work?
A chord of a circle subtends an angle of 60° at the circumference of the circle. What is the ratio of the radius of the circle to the length of the chord respectively?
A sum of 4800 is divided among A, B and C in the ratio 3:4:5. By how much is B’s share more than A’s share?
A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%, B decreases his capital by 50%, and C leaves the capital unchanged. At the end of the year, if the total profit is Rs. 33,000, find the share of B.
The expenditure of a company on five heads A, B, C, D and E is in proportion to 3:5:7:11:? respectively. The expenditure on E is equal to the arithmetic mean of the expenditures on A and D. If the expenditure on C exceeds that on B by ₹18,000, find the total expenditure of the company.
The base of a right pyramid is an equilateral triangle with side 10 cm, and its vertical height is 24 cm. Find the volume (in cm³) of the pyramid.
A hemispherical tank is full of water. It is connected to a pipe that empties it at a rate of 7 litres per second. How much approximate time (in minutes) will it take to empty half the tank if the internal radius of the tank is 2.1 meters? (Use π = 22/7 and 1 m³ = 1000 liters)
If 3x − ky + 8 = 0 and 9x − 18y + 20 = 0 have no solution, find k.
A number is chosen at random from the set {1, 2, 3, …, 120}. What is the probability that the number chosen is divisible by 6 or 8 but not divisible by 24?
If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
At what rate of interest per annum will a sum of Rs.15,625 amount to Rs.19,683 in 1 year and 6 months, if the interest is compounded half-yearly?
The diagonals of three faces of a rectangular parallelepiped that meet at a single corner measure √5 cm, √10 cm, and √13 cm. What is the volume of this parallelepiped?
In an equilateral triangle, the circumcenter coincides with which of the following?
A rectangle has an area of 48 cm² and a perimeter of 28 cm. If the midpoints of the sides of the rectangle are joined to form a rhombus, what will be the area of the rhombus?
The efficiency of Anmol is thrice then Vinay therefore Anmol finish the work in 60 days less then Vinay in how many days they finish the work working together?
A and B can complete a work in 10 and 12 days respectively. They started working together after three day A left the work in how many days the whole work will complete?
Two men can build a wall in 9 hours and 10 hour respectively but if they work together they use 100 less bricks per hour and build the wall in 5 hours find the number of bricks in the wall?
A can do 50% of your work in 16 days, B can do one fourth of the same work in 24 days in how many days they complete the same work working together?
A can do 2/5 of the work in six days and B can do 2/ 3 of the same work in 12 days, A and B work together for six days. C complete the remaining work in eight days, A and C working together will complete the same work in how many days?
The ratio of efficiency of A B and C is 7:5:4 working together they finish the work in 35 days. A and B work together for 28 days the remaining work will be complete by C in how many days?
The ratio of efficiency of A and B is three 3:7 working together they can complete a work in 10.5 days. they work together for 8 days. 60% of the remaining work will be completed by A alone in how many days?
To do a certain work, the ratio of the efficiencies of A and B is 7 : 5. Working together, they can complete the work in 17.5 days. A alone will complete 60% of the same work in
A Can do 1/3 of the work in 15 days, B can do 75% of the same work in 18 days and C can do same work in 36 days B and C work together for eight days in how many days a alone can complete the remaining work