Quantitative aptitude
- The present ages of a father and his son are in the ratio 9 : 4. After 5 years, the ratio of their ages will be 2 : 1. What is the father's present age? Answer: C. 45 years Answer: (C) 45 years Let the ages be 9x and 4x . 9x + 5/4x + 5 = 2/1 ⇒ 9x + 5 = 8x + 10 ⇒ x = 5 . Father = 9 × 5 = 45 ye... 1
- If \(x - \frac{1}{x} = 4\), find the value of \(x^3 - \frac{1}{x^3}\). Answer: A. 76 Answer: (A) 76 x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x) = 64 + 12 = 76 . 1
- If \(2x + 3y = 13\) and \(3x - 2y = 0\), what is the value of \(x + y\)? Answer: D. 5 Answer: (D) 5 From 3x = 2y , y = 3x/2 . Then 2x + 9x/2 = 13 ⇒ 13x/2 = 13 ⇒ x = 2,\ y = 3 . So x + y = 5 . 1
- The average of five consecutive odd numbers is 47. What is the largest of these numbers? Answer: B. 51 Answer: (B) 51 For consecutive odd numbers the average is the middle number, 47. The numbers are 43, 45, 47, 49, 51, so the la... 1
- A boat goes 30 km downstream in 2 hours and 18 km upstream in 2 hours. What is the speed of the stream? Answer: B. 3 km/h Answer: (B) 3 km/h Downstream speed = 15 km/h, upstream speed = 9 km/h. Stream speed = 15 - 9/2 = 3 km/h (boat speed = 12... 1
- The table shows how a family spends its monthly income of ₹48,000.HeadFoodRentEducationTransportSavingsShare of income35%20%15%10%20%How much more money does the family spend on food than on education every month? Answer: D. ₹9,600 Answer: (D) ₹9,600 Difference in share = 35% - 15% = 20% . 20% of ₹48,000 = ₹9,600 . (Food = ₹16,800, Education = ₹7,200.) 1
- Two chords AB and CD of a circle intersect at a point P inside the circle. If AP = 6 cm, PB = 4 cm and CP = 3 cm, find PD. Answer: D. 8 cm Answer: (D) 8 cm Intersecting chords theorem: AP × PB = CP × PD . 6 × 4 = 3 × PD ⇒ PD = 8 cm. 1
- The diagonals of a rhombus are 16 cm and 12 cm long. What is its perimeter? Answer: B. 40 cm Answer: (B) 40 cm The diagonals of a rhombus bisect each other at right angles, so each side = √(8² + 6²) = 10 cm. Perimete... 1
- A solid metallic sphere of radius 6 cm is melted and recast into a cone whose base radius is 6 cm. What is the height of the cone? Answer: C. 24 cm Answer: (C) 24 cm Volumes are equal: 4/3π (6)³ = 1/3π (6)² h ⇒ h = 4 × 216/36 = 24 cm. 1
- A and B start a business with ₹24,000 and ₹36,000 respectively. After 4 months, A invests ₹12,000 more. At the end of the year the total profit is ₹34,000. What is A's share of the profit? Answer: A. ₹16,000 Answer: (A) ₹16,000 A's capital-months = 24000 × 4 + 36000 × 8 = 384000 . B's = 36000 × 12 = 432000 . Ratio = 384 : 432 =... 1
- A trader sells two articles for ₹4,800 each. On one he gains 20% and on the other he loses 20%. What is his overall gain or loss percentage? Answer: D. 4% loss Answer: (D) 4% loss CP of first = 4800/1.2 = 4000 ; CP of second = 4800/0.8 = 6000 . Total CP = 10000, total SP = 9600. L... 1
- Two successive discounts of 20% and 15% are equal to a single discount of: Answer: C. 32% Answer: (C) 32% Single discount = 20 + 15 - 20 × 15/100 = 35 - 3 = 32% . 1
- At what rate of simple interest per annum will a sum of money double itself in 8 years? Answer: B. 12.5% Answer: (B) 12.5% To double, SI = P. P = P × R × 8/100 ⇒ R = 100/8 = 12.5% . 1
- What is the compound interest on ₹15,625 for 3 years at 8% per annum, compounded annually? Answer: C. ₹4,058 Answer: (C) ₹4,058 Amount = 15625 × (27/25)³ = 15625 × 19683/15625 = 19683 . CI = 19683 - 15625 = 4058 . (₹3,750 is the si... 1
- 12 men or 18 women can complete a piece of work in 14 days. In how many days will 8 men and 16 women together complete the same work? Answer: D. 9 days Answer: (D) 9 days 12 men = 18 women, so 1 man = 1.5 women. 8 men + 16 women = 12 + 16 = 28 women. Work = 18 × 14 = 252 wo... 1
- A car covers 360 km in 6 hours. By how much must its speed be increased to cover the same distance in 4 hours? Answer: C. 30 km/h Answer: (C) 30 km/h Present speed = 360/6 = 60 km/h. Required speed = 360/4 = 90 km/h. Increase = 30 km/h. 1
- Find the value of \(\tan 15^\circ \times \tan 30^\circ \times \tan 45^\circ \times \tan 60^\circ \times \tan 75^\circ\). Answer: A. 1 Answer: (A) 1 tanθ × tan(90^° - θ) = tanθ × cotθ = 1 . So tan 15^° tan 75^° = 1 , tan 30^° tan 60^° = 1 and tan 45^° = 1 . Prod... 1
- What is the least number which, when divided by 12, 15, 20 and 54, leaves a remainder of 8 in each case? Answer: A. 548 Answer: (A) 548 LCM(12, 15, 20, 54) = 540. Required number = 540 + 8 = 548 . 1
- How many numbers between 100 and 300 are exactly divisible by 7? Answer: D. 28 Answer: (D) 28 Multiples of 7 up to 299: lfloor 299/7 rfloor = 42 . Up to 100: lfloor 100/7 rfloor = 14 . Count = 42 - 14 = 28... 1
- What is the unit digit of \(3^{65} \times 7^{42}\)? Answer: B. 7 Answer: (B) 7 Unit digits of powers of 3 cycle 3, 9, 7, 1; 65 = 4 × 16 + 1 , so 3⁶⁵ ends in 3. Powers of 7 cycle 7, 9, 3, 1; 42... 1
- If 35% of a number is 147, what is 60% of that number? Answer: D. 252 Answer: (D) 252 Number = 147 × 100/35 = 420 . 60% of 420 = 252 . (Shortcut: 147 × 60/35 = 252 .) 1
- In an election between two candidates, the winner got 58% of the valid votes and won by 1,920 votes. What was the total number of valid votes? Answer: B. 12,000 Answer: (B) 12,000 Loser got 42%. Margin = 58% - 42% = 16% of valid votes = 1920 . Total = 1920/0.16 = 12000 . 1
- Simplify: \(\frac{3}{4}\) of \(\frac{8}{9}\) of 405 + 25% of 240 Answer: A. 330 Answer: (A) 330 3/4 × 8/9 × 405 = 2/3 × 405 = 270 . 25% of 240 = 60. Total = 330 . 1
- Find the value of \(\frac{0.6 \times 0.6 \times 0.6 + 0.4 \times 0.4 \times 0.4}{0.6 \times 0.6 - 0.6 \times 0.4 + 0.4 \times 0.4}\). Answer: C. 1 Answer: (C) 1 Use a³ + b³/a² - ab + b² = a + b . With a = 0.6, b = 0.4 : value = 0.6 + 0.4 = 1 . 1