IIT JEE Practice Question and Answer
8Q: Rajan's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Rajan's daughter and Rajan's mather ? 2171 05b5cc72ce4d2b4197774f773
5b5cc72ce4d2b4197774f773- 132 yearsfalse
- 248 yearsfalse
- 362 yearsfalse
- 450 yearstrue
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Answer : 4. "50 years"
Explanation :
Answer: D) 50 years Explanation: Let Rajan's present age be 'x' years.=> Then his daughter's present age is = x/3 years.His mother's present age = 13x/9 yearsNow, according to the question,x + x/3 + 13x/9 = 125=> x = 125x9/25 = 45Therefore, required difference = 13x/9 - x/3 = 13x - 3x/9 = 10x/9=> 10 x 45/9 = 50 years.
Q: The area of a square is 1024 sq.cm. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is 12 cm less than the side of this square ? 1257 05b5cc72ce4d2b4197774f76e
5b5cc72ce4d2b4197774f76e- 114:9false
- 213:12false
- 316:5true
- 417:13false
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Answer : 3. "16:5"
Explanation :
Answer: C) 16:5 Explanation: Area of a square SxS = 1024 => S = 32 cmLength of the rectangle = 32x2 cm = 64 cmBreadth of the rectangle = 32 - 12 = 20 cmRequired ratio = 64 : 20 = 16 : 5
Q: Statement : Let there be a signboard also indicating the directions and instructions. Assumptions :a) Signboard can be prepared without using any language.b) Signboard is the only effective tool to indicate directions. 1658 05b5cc72ce4d2b4197774f769
5b5cc72ce4d2b4197774f769- 1Both a and b are not sufficienttrue
- 2Only a is sufficientfalse
- 3Only b is sufficientfalse
- 4Both a and b are sufficientfalse
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Answer : 1. "Both a and b are not sufficient"
Explanation :
Answer: A) Both a and b are not sufficient Explanation: The statement doesn't give any clue to the use of language. Hence a is not implicit. b is also not implicit because in the sentence 'only' indicates false meaning.
Q: The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ? 1851 05b5cc72ce4d2b4197774f764
5b5cc72ce4d2b4197774f764- 180 degreesfalse
- 260 degreestrue
- 3120 degreesfalse
- 440 degreesfalse
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Answer : 2. "60 degrees"
Explanation :
Answer: B) 60 degrees Explanation: Given the angles of a quadrilateral are in the ratio of 2:4:7:5Let the angles of a quadrilateral are 2x, 4x, 7x, 5xBut we know that sum of the angles = 360 degrees.=> 2x + 4x + 7x + 5x = 360=> x = 20Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.One of the angle of the triangle = 2 x 40 = 80 degreesThe other angle is 180 - (40 + 80) = 60 degrees. Hence the second largest angle of the triangle is 60 degrees.
Q: Train K crosses a stationary Train L in 50 seconds and a pole in 20 seconds with the same speed. The length of the Train K is 240 meters. What is the length of stationary Train L ? 916 05b5cc72ce4d2b4197774f75f
5b5cc72ce4d2b4197774f75f- 160 mtsfalse
- 2120 mtsfalse
- 3240 mtsfalse
- 4360 mtstrue
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Answer : 4. "360 mts"
Explanation :
Answer: D) 360 mts Explanation: Speed of the Train K is given by s = d/t = 240/20 = 12 m/sDistance covered by Train K in 50 seconds = 12 x 50 = 600 mts.But it crosses Train L in 50 seconds Therefore, the length of the Train L is = 600 - 240 = 360 mts.
Q: In a test, minimum passing percentage for girls and boys is 35% and 40% respectively. A boy scored 483 marks and failed by 117 marks. What is the minimum passing marks for girls ? 1274 05b5cc72ce4d2b4197774f75a
5b5cc72ce4d2b4197774f75a- 1625false
- 2525true
- 3425false
- 4325false
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Answer : 2. "525"
Explanation :
Answer: B) 525 Explanation: Given 40% minimum passing marks for boys = 483 + 117 = 600=> 1% = 600/40 => 100% = 600 x 100/40 = 1500Minimum passing marks for girls = 35% of 1500 = 35 x 1500/100 = 525.
Q: Deepa started a business in 2009 by investing Rs.50,000. She invested Rs. 20,000 as additional amount in 2010 and her friend Sushma joined her with an amount of Rs.70,000. Deepa invested another Rs. 20,000 in 2011 and Avanthi joined them with Rs. 70,000. At the end of these 3 years, they earned a profit of Rs. 3,00,000. Find Sushma's share ? 3409 05b5cc72ce4d2b4197774f750
5b5cc72ce4d2b4197774f750- 1Rs. 75,000false
- 2Rs. 85,000false
- 3Rs. 98,000false
- 4Rs. 1,00,000true
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Answer : 4. "Rs. 1,00,000"
Explanation :
Answer: D) Rs. 1,00,000 Explanation: Deepa invested Rs.50,000 for 12 months, Rs.(50000 + 20000) for 12 months and Rs.(50000 + 20000 + 20000) for 12 months.i.e, she invested Rs.50,000 for 12 months, Rs.70000 for 12 months and Rs.90000 for 12 months.Sushma invested Rs. 70000 for 2 years; i.e, Rs.70000 for 24 monthsAnd, Avanthi invested Rs.70000 for 1 year; i.e, Rs. 70000 for 12 months. Their investing ratio:Deepa : Sushma : Avanthi = (50,000 x 12 + 70000 x 12 + 90000 x 12):(70000 x 24):(70000 x 12)= (25,20,000):(16,80,000):(8,40,000) = 252:168:84 = 3:2:1 Total profit for 3 years = Rs.3,00,000Therefore, Sushma's share = Rs.(3,00,000 x 2 /(3+2+1)) = Rs.(3,00,000 x 2/6) = Rs.1,00,000.
Q: Twelve percent of Kalyan's monthly salary is equal to the sixteen per cent of Nandu's monthly salary. Sarnesh's monthly salary is half that of Nandu's monthly salary. If sarnesh's annual salary is Rs. 1.08 lacs, What is Kalyan's monthly salary ? 1378 05b5cc72ce4d2b4197774f746
5b5cc72ce4d2b4197774f746- 115,000false
- 236,000false
- 324,000true
- 412,500false
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Answer : 3. "24,000"
Explanation :
Answer: C) 24,000 Explanation: Let K = Kalyan's monthly salaryN = Nandu's monthly salaryS = Sarnesh's monthly salary.Then from given data, 12% of K = 16% of NS = N/2 => N = 2SK = 16/12 x N = 16/12 x 2S= 16/6 x 1.08/12 = 16/6 x 0.09 = 0.24 lacs = 24,000