### List of Posts

This is the complete list of categories of posts written during Mar 2020. They have been ordered by the publish date, with the most recent first.

*Published: 01-Mar-2020*In ΔABC, P is a point on BC such that BP : PC = 4 : 11. If Q is the midpoint of BP, then ar(ΔABQ) : ar(ΔABC) is equal to?*Published: 01-Mar-2020*If $\displaystyle \sqrt x + \frac{1}{\sqrt x} = \sqrt 6$, then $\displaystyle x^2 + \frac{1}{x^2}$ =?*Published: 02-Mar-2020*An article is sold for Re 288 after successive discounts of 25% and x%. If the marked price of the article is Re 480, what is the value of x?*Published: 02-Mar-2020*In a class of 50 students, 40% are girls. The average marks of the whole class are 64.4 and the average of the boys' marks is 62. What is the average marks of the girls?*Published: 03-Mar-2020*If 2 sinθ = 5 cosθ, then (sinθ + cosθ)/(sinθ - cosθ)=?*Published: 03-Mar-2020*The efficiencies of A, B and C are in the ratio of 5 : 3 : 2. Working together, they can complete a task in 21 hours. In how many hours will B alone complete 40% of that task?*Published: 03-Mar-2020*The value of $\displaystyle \sin^2 32\degree +$ $\displaystyle\sin^2 58\degree -$ $\displaystyle \sin 30\degree +$ $\displaystyle \sec^2 60\degree$ is equal to?*Published: 03-Mar-2020*Chords AB and AC subtend angles of 110° and 130° at the center of a circle as shown. The angle BAC = ?*Published: 03-Mar-2020*A, B and C can do a work in 24, 12 and 15 days respectively. All start a work together. After 3 days B and C leave the work. How many days will A take to complete the work?*Published: 04-Mar-2020*If 1005x4 is divisible by 8, find the value of x?*Published: 04-Mar-2020*If the radius of a circle is 42 cm, how much distance will be covered by making 8 rounds?*Published: 04-Mar-2020*The average of first 5 numbers out of 6 numbers is equal to 7 times the 6-th number. If average of all the numbers is 138, then what is the 6-th number?*Published: 04-Mar-2020*A completes a job in 40 days. The efficiency of B is 25% more than that of A. C is 28% more efficient than B. The work can be completed by A, B and C together in 5 days. How long will B alone take to complete the same work?*Published: 04-Mar-2020*If x - y = 4, and xy = 45, what is the value of (x³ - y³)?*Published: 04-Mar-2020*if x = 4cos A + 5sin A, and y = 4sin A - 5cos A, then find the value of (x² + y²)?*Published: 04-Mar-2020*Radii of two cylinders are in the ratio 4 : 5 and their heights are in the ratio 9 : 8. The ratio of their volumes is?*Published: 04-Mar-2020*ABC is a triangle with an area of 44 sq. cm. If D and E are the midpoints of BC and AB respectively, then the area of triangle BDE is?*Published: 04-Mar-2020*In a triangle ABC, M and N are points on AB and AC respectively, such that MN is parallel to BC and AN : NC is 4 : 5. If the area of the quadrilateral MNCB is 130 sq. units, then what is the area of triangle MAN?*Published: 04-Mar-2020*Re 4300 becomes Re 4644 when invested at SI for 2 years. What will Re 10104 become when invested for 5 years at the same plan?*Published: 04-Mar-2020*Given x + y = 8, y + z = 13, z + x = 17, then the value of x²/yz = ?*Published: 04-Mar-2020*If $\displaystyle x^{2a} = y^{2b} = z^{2c}$ and x² = yz, then (ab + bc + ca)/bc = ?*Published: 04-Mar-2020*If 6 tan A = 5, then (8 sin A- 4 cos A)/(cos A - 2 sin A) = ?*Published: 04-Mar-2020*Raj sells an item at Rs. x and incurs a loss of 10%. Had he sold it at a profit of 20%, he would have got Rs. 332 more. What is x?*Published: 05-Mar-2020*An item marked at Rs. 350 is sold at a discount of 28%. What is the cost price if the profit is 12%?*Published: 05-Mar-2020*Length of a rectangle is increased by 40%, and the breadth reduced by 20%. Find the percent change in the area?*Published: 05-Mar-2020*In a class of 640 the ratio of boys to girls is 5 : 3. If the number of girls is increased by 30, how should the strength of boys be changed so that the new ratio is 14 : 9?*Published: 05-Mar-2020*A train crosses a pole in 18 seconds, but a 170 meter long bridge in 36 seconds. What is the speed of the train?*Published: 05-Mar-2020*If (secθ + tanθ)/(secθ - tanθ) = 5/3, what is the value of (cosecθ + cotθ)/(cosecθ - cotθ)?*Published: 05-Mar-2020*If x⁴ + x²y² + y⁴ = 21, x² + xy + y² = 7, then the value of (1/x² + 1/y²) = ?*Published: 05-Mar-2020*A circular park is in the form of a ring of inner and outer circumference 440 m and 506 m. The cost of levelling at Rs. 6 per square meter is?*Published: 05-Mar-2020*200 leaves a remainder 8 when divided by x. How many such x are possible?*Published: 05-Mar-2020*Speed of a train A is 20% more than that of train B. After meeting, they take x and 2-1/2 hours respectively to reach their destinations. What is x?*Published: 06-Mar-2020*If x² - 3x + 1 = 0, then x^6 + 1/x^6 = ?*Published: 06-Mar-2020*What is the value of $\displaystyle \sec(85 + \theta)$ - $\displaystyle \cosec(5 - \theta)$ + $\displaystyle \tan(35 + \theta)$ - $\displaystyle \cot(55 - \theta)$*Published: 06-Mar-2020*An amount x is invested at 10% p.a., and gives Rs. 1201.2 in 2-1/3 years. What is x?*Published: 06-Mar-2020*In-radius of a triangle is 3 cm. What is the perimeter if its area is 15 sq. cm?*Published: 06-Mar-2020*Two containers of equal capacity are filled with orange juice to the extent of 35% and 33-1/3%. After some time apple juice is added to both the containers so as to fill them completely. Both these containers are then emptied into another container. What is the percentage of apple juice in the new container?*Published: 06-Mar-2020*What is the perimeter of an equilateral triangle whose each median is 2√3 cm?*Published: 06-Mar-2020*An item is marked at 25% higher than the CP. What will be the percentage gain or loss If the CP increases by 20% and the marked price by 10%?*Published: 07-Mar-2020*If 2 sinθ + 15 cos²θ = 7, and θ is an acute angle, then the value of (tanθ + cosecθ + secθ) is?*Published: 07-Mar-2020*Average of first four numbers is 3 times the fifth number. The average of all five numbers is 85.8. What is the fifth number?*Published: 07-Mar-2020*Given that ΔABC ~ ΔDEF, and AM and DN are the altitudes of these triangles. The ratio of areas of ΔABC and ΔDEF is 9 : 25. Then (DN + AM)/(DN - AM) =?*Published: 07-Mar-2020*A circle is inscribed in a quadrilateral as shown. If AB = 7 cm, BC = 6 cm and CD = 8 cm, then the length of AD is?*Published: 07-Mar-2020*A certain amount yields an interest of Rs. 1200 when invested for 3 years at a simple interest of 5%. Calculate the interest if the interest had, instead, been compounded annually at the same rate?*Published: 07-Mar-2020*Average of 5 consecutive even numbers is X. What will be the average if next 5 consecutive even numbers are also added?*Published: 07-Mar-2020*What is 1 + 4 + 9 + 16 + 25 + . . . n²?*Published: 07-Mar-2020*Present ages of two persons A and B differ by 6 years, but are in the ratio 5 : 6. The ratio of their ages 5 years hence will be?*Published: 07-Mar-2020*Two racers are running in the same direction at speeds of 100 m/min and 120 m/min. What is the length of the track if the difference between their travel times is 10 minutes?*Published: 07-Mar-2020*In a triangle ABC, AP is an angle bisector and AB = 4, AC = 6, and BP = 3. The length of CP is?*Published: 07-Mar-2020*Simplify (a + b + c + d)² - (a - b - c - d)²*Published: 07-Mar-2020*What is the surface area of a hemisphere of radius 7cm?*Published: 07-Mar-2020*A and B can complete a work in 20 and 25 days respectively. Both start together, but B leaves after 5 days. How many days will A take to complete the remaining work?*Published: 07-Mar-2020*A person gains 5% by selling 6 articles for a total price of Rs. 63000. For how much should he sell 8 articles so as to make a profit of 15%?*Published: 07-Mar-2020*If 98x238 is divisible by 11, then what is the value of x?*Published: 07-Mar-2020*If sinθ = 1/4, then the value of 8(cosθ + cotθ) is?*Published: 07-Mar-2020*A chord is drawn inside a circle of radius 5 cm. What is the length of the chord if its distance from the center of the circle is 3 cm?*Published: 07-Mar-2020*In an isosceles triangle ABC, AB = AC. If angle A is 52°, then find the value of angle B?*Published: 07-Mar-2020*If 2sinθ - 6√3tanθ + 5 = 0, then the value of (tan2θ + cos2θ) is?*Published: 07-Mar-2020*Two numbers A and B are in the ratio 4 : 7. If B is 28, then A is?*Published: 08-Mar-2020*If $\displaystyle 5x + \frac {1}{3x} = 4$, then $\displaystyle 9x^2 + \frac{1}{25x^2}$ =?*Published: 08-Mar-2020*ABCD is a cyclic quadrilateral in which AB = 16.5 cm, AD = 11 cm and CD = 19.8 cm. If AC bisects BD, then what is the measure of BC?*Published: 08-Mar-2020*If numbers (2x+1), (x+2), 2 and 5 are in proportion, then mean proportion of 3.5(1-x) and 8(1+x) is?*Published: 08-Mar-2020*A seller gives a discount of 18% on MRP. By how much percentage above CP, should he mark up so as to gain 6.6% profit on the cost price?*Published: 09-Mar-2020*If a + b + c = 11, ab + bc + ca = 3 and abc = -135, then a³ + b³ + c³ =?*Published: 09-Mar-2020*If secθ - tanθ = x/y, find the value of sinθ?*Published: 10-Mar-2020*A sum of Rs 12000 is given at 8% per annum for 2-5/8 years, compounded annually. Find out the compound interest for the given time period.*Published: 10-Mar-2020*Sushma bought 12 tables and 9 chairs for Rs.15,400. She sold the tables at a profit of 10% and the chairs at a profit of 20%. If her total gain was Rs. 2080, then the total cost of the 3 chairs was?*Published: 10-Mar-2020*A shopkeeper gives two successive discounts of 25% and 20% respectively and still earns 20% profit. If no discount was given by the shopkeeper, then the profit% would have been?*Published: 10-Mar-2020*In a right-triangle ABC, angle A = 90 degree, AB = 7cm, AC = 24cm. M is the mid-point of BC and AD⊥BC. Find AM : AD?*Published: 11-Mar-2020*In triangle ABC, ∠C = 68°, ∠B = 32°. The external angle bisectors of ∠B and ∠C meet at point O. Find ∠BOC.*Published: 11-Mar-2020*In a triangle ABC, AB = AC. A circle is drawn from vertex B such that it touches the side AC at D (where D is the mid-point of AC) and it cuts the side AB at E where AE = 2.5cm. Find the length of side AB.*Published: 11-Mar-2020*When 732 is divided by x, the remainder is 12. How many such values of x are possible?*Published: 11-Mar-2020*If 5 sin²θ + 14 cosθ = 13, then (secθ - tanθ)/(secθ + tanθ)=?*Published: 11-Mar-2020*A can do a work in 30 days. Efficiency of B is 25% more than A and efficiency of C is 20% more than B. They work together for 3 days. In how many days B will complete remaining work?*Published: 11-Mar-2020*A person can save 15% of his income. If his income increases by 20% and still he saves the same amount as before, the percentage increase in his expenditure is?*Published: 11-Mar-2020*A conical tent of circular base with perimeter 66m and height 36m is made of canvas. Find the area of canvas required to make the tent.*Published: 12-Mar-2020*The ratio of boys and girls in a class is 7:6. When 4 new boys joined the class, 3 girls left it and the ratio of boys and girls becomes 4:3. Find the number of total students that were in the class initially.*Published: 12-Mar-2020*If $\displaystyle 30x^2 - 15x + 1 = 0$, then $\displaystyle 25x^2 + \frac{1}{36x^2}=?$*Published: 12-Mar-2020*If a + b + c = 7, ab + bc + ca = -6, then a³ + b³ + c³ - 3abc =?*Published: 12-Mar-2020*The marked price of an article is Rs 740. The shopkeeper sells the article at Rs 566.10 by giving two successive discounts of 15% and x% respectively. Find the value of x.*Published: 12-Mar-2020*A can complete a work in (d + 8) days and B can complete the same work in (d + 18) days. Working together, they can complete this work in d days. What is the value of d?*Published: 14-Mar-2020*In a circle, AB and CD are two chords. When they are extended, they meet at a point P outside the circle such that AB = 7cm, BP = 4.2cm and DP = 2.8cm. Find the length of chord CD?*Published: 14-Mar-2020*The average weight of N persons is 56.5 kg. When 5 more persons join, the average increases by 0.55 kg. If the average of 5 new members is 64.2 kg, then N is?*Published: 14-Mar-2020*PRT is a tangent to a circle with center O touching the circle at R. Diameter SQ is produced to meet P. If angle PRQ = 28 degree, then find angle SPR.*Published: 14-Mar-2020*The difference between the compound interest compounded half-yearly and compound interest compounded yearly is Rs 88.50 at the rate of 10% in 1 year. What is the SI on the same sum at the same rate per annum for 1-2/3 year?*Published: 14-Mar-2020*A cylindrical vessel of base radius 30 cm and height 42 cm is filled with a liquid. This liquid is poured into a cuboidal container whose length and breadth are 17 cm and 37 cm respectively. The height of the cuboidal vessel upto which the liquid will be filled?*Published: 14-Mar-2020*The value of $\displaystyle \frac{\tan^2\theta - \sin^2 \theta}{2 + \tan^2 \theta + \cot^2 \theta}$ is?*Published: 15-Mar-2020*A's income is 60% less than B and A's expenditure is 60% of B's expenditure. If A's income is 70% of B's expenditure, then find the ratio of savings of A and B.*Published: 15-Mar-2020*If x + y + z = 3, and x² + y² + z² = 101, then √ (x³ + y³ + z³ - 3xyz) =?*Published: 15-Mar-2020*A sold an article to B at a loss of 20%. B sold it to C at a profit of 12.5%. C sold it to D at a loss of 8%. D pays Rs 248.4 for that article. Find the difference of loss incurred by A and C?*Published: 16-Mar-2020*A sum of Re. x is divided between A, B, C and D in the ratio 1/3 : 1/5 : 1/6 : 1/9. The difference between the amount of B and D is Re. 832. Find the value of x?*Published: 16-Mar-2020*4 men and 6 women can do a work in 5 days. 3 men and 4 women can do the same work in 7 days. How many men will assist 25 women to complete 2-1/2 times the same work in 5 days?*Published: 17-Mar-2020*If SP of an article is 80% more than CP and a discount of 10% is given on MP. What is the ratio of CP : MP?*Published: 20-Mar-2020*A field whose area is 2400√3 sq. m is in the shape of a regular hexagon. If the cost of fencing the field is Rs 16.80/m, then find the total cost required to completely fence the field?*Published: 20-Mar-2020*A sum of Rs 8000 is invested at the rate of 10% amounts to Rs 9261 if compounded half-yearly. What will be the amount if the rate of interest is doubled?*Published: 20-Mar-2020*Chords AB and CD of a circle intersect at E. If AE = 12cm, BE = 20.25cm and CE = 3DE. Find the length of CE?*Published: 20-Mar-2020*If 2x² + y² + 8z² - 2√2xy + 4√2yz - 8zx = (Ax + y + Bz)², then the value of A² + B² - AB =?*Published: 22-Mar-2020*How many numbers are there between 200 and 800 that are neither divisible by 5 nor by 7?*Published: 22-Mar-2020*If 12x² - 21x + 1 = 0, then the value of 9x² + 1/16x² =?*Published: 22-Mar-2020*Two circles of radius 5 cm and 7 cm intersect at two points A and B. if the distance between the centres of two circles is 10 cm, then find the length of the common chord.*Published: 22-Mar-2020*If 7cos²θ + 3sin²θ = 6, then (cot²θ + sec²θ )/(tan²θ - sin²θ) = ?*Published: 22-Mar-2020*The distance between two places is 144 km. If two cars are running in the same direction then the faster car takes over the slower car in 12 hours whereas if the cars travel in opposite directions then they cross each other in 9/8 hours. Find the speed of the faster car?