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URVASHI GARG

A goods train 158 metres long and travelling at the speed of 32 km per hr. leaves Delhi at 6 am. Another mail train 130 metres long and travelling at the average speed of80 km per hr. leaves Delhi at 12 noon and follows the goods train. At what time will the mail train completely cross the goods train?

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(1)4hours (2)4 hours 21.6 sec. (3)5 hours 21.6 sec. (4) None of these Solution: The goods train leaves Delhi at 6 am and mail train at 12 noon, hence after 6 hours The distance covered by the goods train in 6 hours at 32 km per hr.  = 32*6= 192 kms The relative velocity of […]

A goods train 158 metres long and travelling at the speed of 32 km per hr. leaves Delhi at 6 am. Another mail train 130 metres long and travelling at the average speed of80 km per hr. leaves Delhi at 12 noon and follows the goods train. At what time will the mail train completely cross the goods train? Read More »

If x = √3-√2/√3+√2 and y = √3+√2/√3-√2 find the value of x3+y3 :

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(1) 807 (2) 907 (3) 970 (4)870 Solution: Rationallsing the denominators. we have x=√3-√2/√3+√2*√3-√2/√3-√2 =(√3-√2)2/(√3)2-(√2)2 = 3+2-2√3*√2/3-2 = 5-2√6 and,  y=√3+√2/√3-√2*√3+√2/√3+√2 = (√3+√2)2/(√3)2-(√2)2 = 3+2+2√3*√2/3-2 = 5+2√6 :.  x+ y = 5-2√6+5+2√6 = 10 and,  xy= (5-2√6) (5+2√6) = 52-(2√6)2 =25-24=1 x3+y3 =(x+y)3-3xy (x+ y) = 103– 3 *10 = 1000 – 30 =970 Then the option is

If x = √3-√2/√3+√2 and y = √3+√2/√3-√2 find the value of x3+y3 : Read More »

The average age of 30 students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is:

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(1) 11 years 2 months (2) 13 years 6 months (3) 12 years 4 months (4) 10 years 4 months Solution: Total age of initial 30 students = 14years 4 months * 30 = 430 years Total ageof 35 students = 13years 9 months * 35 = (455 + 26)years 3 months = 481 years

The average age of 30 students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is: Read More »

My grandfather was 9 times older than me 16years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was:  (1) 3: 8 (2) 2: 5 (3) 1: 2 (4) 1: 5

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Solution: 16 years ago, My age = x years My grandfather’s age = 9x years After 8 years from the present, 9x+ 16+8=3(x+8+ 16) ⇒9x+ 24 = 3x+ 24 + 48 ⇒9x+24=3x+72 ⇒9x- 3x= 72 -24  ⇒6x= 48 ⇒x=48/6 = 8 Required ratio 8 years ago, = (x+ 8) : (9x+ 8) = (8 +

My grandfather was 9 times older than me 16years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was:  (1) 3: 8 (2) 2: 5 (3) 1: 2 (4) 1: 5 Read More »

The ratio of the ages of two persons is 4 : 7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages (in years) is

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(1) 110 (2) 100 (3) 70 (4) 40k Solution: Ages of the persons = 4x and 7x years. :. 7x-4x=30 ⇒3x=30 ⇒ x=10 :. Sum of their ages = 4x+7x = 11x years = 11*10= 110 years Then the option is (1) 110

The ratio of the ages of two persons is 4 : 7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages (in years) is Read More »

A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base 8 cm. Approximately how much paper has been used to make it? (Use√3 = 1.732)

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(1) 539.712 cm2 (2) 538.721 em2 (3) 540.712 em2 (4) 539.217 cm2 Solution: Area of paper=Area of square +Area of equilateral triangle =1/2 (diagonal)2+ √3/4*(side)2 =1/2*32*32+√3/4*8*8 = 512 + 16 * 1.732 = 512 + 27.712 = 539.712 cm2 (Note: Diagonal of a square =√2 side) Then the option is (1) 539.712 cm2

A kite in the shape of a square with a diagonal 32 cm attached to an equilateral triangle of the base 8 cm. Approximately how much paper has been used to make it? (Use√3 = 1.732) Read More »

800 chocolates were distributed among the students of a class. East student got twice as many chocolates as the number of students in the class. The number of students in the class was :

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(1) 25 (2) 30 (3) 35 (4) 20 Solution: Let the number of students be n. So, each of n students got 2n chocolates Total no. of chocolates = (2n)*n = 800 ⇒ 2n2 =800 ⇒ n2=400 ⇒ n=20 Then the option is (4)

800 chocolates were distributed among the students of a class. East student got twice as many chocolates as the number of students in the class. The number of students in the class was : Read More »

The ratio of number of boys to that of girls in a group becomes 2: 1when 15girls leave. But. afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was

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(1) 20 (2)30 (3)40 (4)50 Solution: Let the original number of boys and girls be x and y respectively. Then x/y-15=2/1 ⇒ x = 2y – 30    ……….(i) Again, x-45/y-15=1/5 ⇒ 5x-225=y-15 ⇒ 5x= y-15+225 ⇒ 5(2y-30) = y+210 [From equation (i)) ⇒ 10y-150=y+210 ⇒ 10y-y=210+150 ⇒ 9y = 360 ⇒ y=360/9 = 40

The ratio of number of boys to that of girls in a group becomes 2: 1when 15girls leave. But. afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was Read More »