SI, CI
A sum lent at 24% p.a. simple interest yields Rs. 180 more interest than when lent at 20% p.a. compound interest in two years. Find the sum. TITA type i.e. Type In The Answer type 4500 Let the amount be x Rs. x(124/100) - x(1 +20/100 ) =180 x=4500
Loan paid in 2 years at CI
Ravi borrows a sum of Rs. 64,000 at 5% p.a. compounded annually. At the end of one year, he repays a certain amount and he repays the balance amount of Rs. 35,700 at the end of the second year. What amount did he repay at the end of the first year? TITA type i.e. Type In The Answer type 33200 Compound interest of the first year = 5% of 64,000 = 3,200 Amount at end of 1st year = 64,000 + 3,200 = 67,200. Suppose amount repaid at end of first year is x, the principal for second year will be (67,200 – x) And amount at end of 2nd year will be (67,200 – x) × 1.05 This is given to us as 35,700 $$ \begin{aligned} & (67200-X) \times 1.05=35700 \\ & \Rightarrow 67200-X=34000 \\ & \therefore X=33200 \end{aligned} $$ [...]
Intersecting diagonals in a hexagon
Q. A regular hexagon ABCDEF has a side length of 6 cm. BF and BE are diagonals of the hexagon which intersect the diagonal AD at points P and Q respectively. What is the ratio of the area of triangle BPQ to that of the quadrilateral ABDF ? A. \(\frac{1}{8}\) B. \(\frac{1}{6}\) C. \(\frac{1}{7}\) D. \(\frac{1}{4}\) A. \(\frac{1}{8}\) In Δ APB, AB = 6 AP = 3 PB = \(3\sqrt{3}\) AD = BE = 12 So, Δ PBD = 90 BQ = 1/2 BE = 6, QD = 1/2 AD = 6 In Δ PQB opp 60 → PB = \(3\sqrt{3}\) OPP 30 → PQ = \( \frac{3\sqrt{3}}{\sqrt{3}}\) = 3 Area of PQB = \(\frac{1}{2} × PQ × PB\) = \(\frac{1}{2}×3×3\sqrt{3}\) = \(\frac{9\sqrt{3}}{2}\) Area of Quad ABDF = Area of eq Δ BDF + Area of iso Δ ABF = \(\frac{\sqrt{3}}{4}×{(6\sqrt{3}})^{2}+\frac{1}{2}×6×6×\sin 120°\) Ratio = [...]
Equation, Quadratic
Solve for $9^x-90 \times 3^x+729=0$ A. 1, 2 B. 2, 3 C. 3, 5 D. 2, 4 D. 2,4 $\begin{aligned} & 9^x-90 \times 3^x+729=0 \\ \Rightarrow & \left(3^x\right)^2-81 \cdot 3^x-9 \cdot 3^x+729=0 \\ \Rightarrow & 3^x\left(3^x-81\right)-9\left(3^x-81\right)=0 \end{aligned}$ $3^x =81 or 9$ $x=2,4$
Numbers
$\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{\frac{1}{1}+\frac{1}{3^2}+\frac{1}{4^2}}.............\sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$ TITA type i.e. Type In The Answer type 2007 In first bracket, there is 1 * 2 in the denominator. In the second bracket, there is 2*3 in the denominator In the third bracket, there will be 3*4 in the denominator. And in the last bracket, there is 2007*2008 in the denominator. So, no of terms are from 1 to 2007 (2007 terms) or from 2 to 2008 (still 2007 terms). So, 1+1+1+1+1+...(2007 times) = 2007
Profit, Loss
John sells cornflour at the rate of Rs. 5.10 per kg and gains a profit of 20%. If he decreases the price so as to gain only 25 p. per kg, what should be the ratio in which the sales should increase so as to get the same amount of profit? A. 1:03 B.5:17 C.17:05 D.12:17 B.5:17 Cp is 51* 5/6 = 4.25 per kg so earlier the profit was 0.85 per kg now the profit if 0.25 per kg so 0.25 :0.85 = 5:17
Geometry
What is the number of points of intersection of the diagonals of a regular convex polygon (other than the vertices of the polygon) with 7 sides? A. 27 B. 35 C. 31 D. 42 B. 35 As we know that no two diagonals are parallel in the polygon with odd number of sides. If we take any 4 vertices then we get one intersection point. So, we need to select 4 vertices out of 7 vertices. $\mathrm{C}_{\mathrm{4}}^{\mathrm{7}}$ = 35
Venn Diagram
95% of the students in a class have taken Ethics, 80% have chosen Communication skills, 84% have chosen Business laws (BL), and 90% have chosen Public Policy (PP). What is the maximum and minimum percentage of people who have chosen all of the four? A. 80% and 56% B. 95% and 53% C. 80% and 49% D. 80% and 51% C. 80% and 49 % Maximum percentage of people who have chosen all of the four People opting communication skills is , it comprises the smallest percentage of the total available for the overlap of students studying other subjects. minimum percentage of people who have chosen all of the four Max number of students studying 3 subjects or less
Profit, loss
A had purchased a cycle a few years back. He carries out repair of 1000 and sells to B at 10% profit. B repairs for 1000 and sell to C at 10% profit.C spend 1000 and sell to D at 10% profit. D paid Rs. 7634. Find the price of A. TITA type i.e. Type In The Answer type 3000 Rs. C sells good to D, selling price = 7624 and profit% = 10% ⇒ CP of C = 7634 *10/11 = 6940 Now this is cost of C, which includes Rs. 1000 that he spent on repairs. So, C must have paid Rs. 6940 – 1000 = 5940 when he purchased the cycle. Similar situation for B B sells good to C, selling price = 5940 and profit% = 10% ⇒ CP of B = 5940 *10/11 = 5400 Now this is cost of [...]
CAT Preparation Tips for Working Professionals: Balancing Work and Study
Here’s how you ace your CAT prep while keeping your full-time work going If you have a regular 9-5, you must’ve gone looking for CAT preparation tips, Googled tips to balance work and life, and searched a variety of resources to create a prep-plan that works for you. Chances are, you got the same tired advice about creating time, making time, hustling, pulling all-nighters, taking time off of work and similar stuff. Right? Now, while these are not bad ideas, they aren’t great ones either. Why? Well, for one thing, they tend to generalise and assume that everyone is in the same boat, job-wise. Two, they tell you what to do, but never ‘how to’ do it. This basically leaves you with a handful of advice that you don’t know what to do with. Read on to discover two ways you can actually ace your CAT prep, even if [...]