26- 15 मिनट बहुत है - 20 Sept 2nd Shift- SSC CGL Tier-1 Solved Paper by Rohit Tripathi
Summary
This video provides solutions to mathematics questions from the SSC CGL 2025 exam, held on September 20th, Shift 2. It covers a range of topics including arithmetic, algebra, geometry, and trigonometry. Key concepts explained include calculating square roots, partnership investment ratios, salary percentages, compound interest growth, profit/loss on sales with discounts, relative speed, simple interest, geometrical shapes properties, and trigonometric identities. The presenter breaks down each problem step-by-step, often using quick methods and relating them to common mathematical principles.
Key Insights
Calculates the number of triangles formed by diagonals from one vertex of an octagon.
For a polygon with 'n' sides, the number of triangles formed by drawing diagonals from one vertex is n-2. For an octagon (n=8), this results in 8-2 = 6 triangles.
Finds the circumcenter of a right-angled triangle.
The circumcenter of a right-angled triangle lies at the midpoint of its hypotenuse. Given vertices (0,0), (8,0), and (0,6), the hypotenuse connects (8,0) and (0,6). The midpoint is calculated as ((8+0)/2, (0+6)/2) = (4, 3).
Calculates the percentage increase in prism volume with increased base area.
The volume of a prism is given by (Base Area * Height). If the base area is increased by 25% and the height remains the same, the volume will also increase by 25%.
Sections
Arithmetic and Algebra Problems
Calculates square root of 9801 - 1681.
The question involves finding the square root of 9801 minus 1681. 9801 is identified as 99 squared, and 1681 is identified as 41 squared. The calculation is presented as sqrt(9801) - sqrt(1681) = 99 - 41 = 58.
Solves partnership problem with changing investments and ratios.
Three partners P, Q, R invest in a ratio of 6:7:9. After one year, P adds 300, Q adds 25,000, and R adds an unknown amount. Their new investment ratio becomes 8:9:11. The problem is solved by setting up equations based on the ratios and the difference in investments, deducing that 'a' = 35 and then calculating R's initial investment and the added amount.
Determines total salary from charity, investment, and expense distribution.
An employee donates 20% of their salary to charity. Of the remaining amount, 40% goes to investment, and the rest is split between education and travel in a 7:5 ratio. If the travel expense is 6000, the total salary is calculated. The ratio of travel expense to total salary is determined, leading to the calculation of the original salary.
Calculates time for investment to grow 20 times using compound interest.
A certain amount becomes 5 times in 10 years with compound interest. The question asks how long it will take to become 20 times. Using the principle that if (1 + R/100)^10 = 5, then squaring both sides gives (1 + R/100)^20 = 25. The solution implies that 25 times would take 20 years, which is approximated to 20 times as per the question's likely intent or a simplification.
Analyzes profit/loss for software licenses with discounts and freebies.
A software company develops 800 licenses. 50 are given free. Remaining licenses get a 15% discount on the 6000 marked price. A 'buy 9 get 1 free' offer is applied. The calculation involves determining the selling price after discount, the number of paid licenses after the offer, total revenue, and comparing it to the cost (implied purchase cost of licenses) to find the overall gain or loss percentage.
Calculates time for faster motorcyclist to catch up.
Two motorcyclists have a speed ratio. The slower one travels 24 km ahead. Their speed difference is presented as 3 units, equating to 12 km/h. The faster rider needs to cover the 24 km distance at a relative speed of 8 km/h (2 units of speed difference). Time taken is distance/speed = 24/8 = 3 hours. The distance covered by the faster rider in 3 hours is also calculated.
Calculates simple interest on a loan.
A shopkeeper takes a loan of 7500 at 9% simple interest from April 1st and repays it on September 1st. The loan duration is calculated as 5 months (April to September). The simple interest for this period is calculated using the formula SI = (P * R * T) / 100, where T is in months converted to years.
Identifies a number that is both an integer and a whole number.
The question asks to identify a number that is both an integer and a whole number. The answer provided is '0', as whole numbers are non-negative integers (0, 1, 2, ...) and integers include negative numbers, zero, and positive numbers. Therefore, 0 fits both definitions.
Calculates share of profit in a partnership.
Three individuals A, B, and C invest in the ratio 2:3:5. The total profit is divided among them. The question asks for B's share, which is calculated as B's ratio part out of the total ratio sum, multiplied by the total profit.
Calculates paint needed for a pyramid based on surface area and coverage.
A solid pyramid has a total surface area of 48 sq meters. Paint covers 2 sq meters per liter. The basic paint needed is 48 / 2 = 24 liters. An additional 5% is required due to wastage or extra coverage needs, calculated as 1.2 liters. Total paint needed is 25.2 liters.
Calculates the total cost of tiling an L-shaped floor with discount.
An L-shaped floor is made of two rectangular blocks with areas 24 sq meters and 48 sq meters, totaling 72 sq meters. The cost is 450 per sq meter. A 10% discount is applied if more than 70 sq meters are tiled. Since 72 sq meters are tiled, the discount applies. The total cost is calculated based on the total area, rate, and discount.
Solves a problem involving mixing oils and calculating profit/loss.
Two cans contain oil: 40 liters at 50/liter and 60 liters at 60/liter. They are mixed, making 100 liters. 20 liters of this mixture are sold at 70/liter. The total cost of the oils is calculated (40*50 + 60*60 = 2000 + 3600 = 5600). The cost per liter of the mixture is 5600/100 = 56. The revenue from selling 20 liters is 20*70 = 1400. Profit is (Selling Price - Cost Price) = (1400 - 20*56) = 1400 - 1120 = 280.
Determines the value of cos(2a) given a trigonometric identity.
Given the identity cos(a) = 1 - 2sin²(a), which is the double angle formula for cosine, the question asks for the value of cos(2a). By substituting a=0, it's shown that cos(0) = 1 - 2sin²(0), so 1 = 1. Thus, cos(2a) is equivalent to cos(a) in this context, or the identity itself confirms cos(2a).
Finds the equation of a line passing through two points.
The video explains how to find the equation of a line passing through two points (x1, y1) and (x2, y2) using the formula y - y1 = ((y2 - y1) / (x2 - x1)) * (x - x1). An example is worked out with points (1, 2) and (3, 3), resulting in the equation y = 3x - 1.
Solves a trigonometric equation involving sin and cos.
The equation sin(3x) = cos(2x + 10°) is given. Using the identity sin(A) = cos(90° - A), it converts to cos(90° - 3x) = cos(2x + 10°). Equating the angles, 90° - 3x = 2x + 10°, which leads to 5x = 80°, so x = 16°.
Calculates the number of triangles formed by diagonals from one vertex of an octagon.
For a polygon with 'n' sides, the number of triangles formed by drawing diagonals from one vertex is n-2. For an octagon (n=8), this results in 8-2 = 6 triangles.
Finds the circumcenter of a right-angled triangle.
The circumcenter of a right-angled triangle lies at the midpoint of its hypotenuse. Given vertices (0,0), (8,0), and (0,6), the hypotenuse connects (8,0) and (0,6). The midpoint is calculated as ((8+0)/2, (0+6)/2) = (4, 3).
Determines tree's height using shadow lengths.
A person 5 feet tall casts a 4-foot shadow. A tree casts a 20-foot shadow. Assuming similar triangles, the ratio of height to shadow length is constant. So, (height of person / shadow of person) = (height of tree / shadow of tree). (5/4) = (height of tree / 20). Solving for the height of the tree gives 25 feet.
Geometry and Mensuration Problems
Calculates the ratio of areas of a large polygon made of hexagons to a single hexagon.
A large regular polygon is formed by joining six regular hexagons around a common center. If the area of a single hexagon is 'a', the total area of the combined shape is 6a. The ratio of the combined shape's area to a single hexagon's area is 6a / a = 6.
Calculates the total expense to paint a triangular sign board.
A triangular traffic sign board has sides 13, 14, and 15. The semi-perimeter is calculated (13+14+15)/2 = 21. Using Heron's formula, the area is sqrt(21 * (21-13) * (21-14) * (21-15)) = sqrt(21 * 8 * 7 * 6) = sqrt(7056) = 84 sq meters. Painting costs 5 per sq meter, so total expense = 84 * 5 = 420.
Calculates the percentage increase in prism volume with increased base area.
The volume of a prism is given by (Base Area * Height). If the base area is increased by 25% and the height remains the same, the volume will also increase by 25%.
Calculates time to fill a tank by a man and woman working together.
A man fills 4 liters in 3 minutes (rate = 4/3 L/min). A woman fills 3 liters in 4 minutes (rate = 3/4 L/min). Together, their combined rate is (4/3 + 3/4) = (16+9)/12 = 25/12 L/min. To fill 100 liters, time = Total Volume / Combined Rate = 100 / (25/12) = 100 * 12 / 25 = 4 * 12 = 48 minutes.
Number Theory and Ratios
Calculates the difference between the largest and smallest of three numbers in a given ratio.
Three numbers are in the ratio x:y:z. Their average is given. The average is calculated as (sum of numbers) / (count of numbers). This average is equated to the given value to find 'x'. The difference between the largest (5x) and smallest (2x) number is then calculated as 3x.
Miscellaneous
Calculates profit from selling a mixture of oils.
Two oils are mixed. The total cost is calculated based on the quantity and price per liter of each oil. The cost per liter of the mixture is found. Then, the selling price of a portion of the mixture is determined, and profit or loss is calculated by comparing the revenue with the cost of the sold portion.
Ask a Question
*Uses 1 Wisdom coin from your coin balance
