Skip to main content

2

Q1. The difference of two natural numbers is 60. If we get 4 on dividing the bigger by the smaller number, find the numbers.

Solution

Let space the space bigger space natural space number space be space straight x. Then comma space the space smaller space natural space number space equals straight x space minus space 60 According space to space question comma space we space have fraction numerator straight x over denominator straight x space minus space 60 end fraction equals 4 rightwards double arrow straight x equals 4 left parenthesis straight x space minus space 60 right parenthesis rightwards double arrow straight x equals 4 straight x space minus space 240 rightwards double arrow straight x space minus space 4 straight x equals negative 240 rightwards double arrow negative 3 straight x space equals space minus 240 rightwards double arrow 3 straight x space equals space 240 rightwards double arrow straight x space equals space 240 over 3 equals 80 rightwards double arrow space straight x space minus space 60 space equals space 80 space minus space 60 space equals space 20 Thus comma space the space required space numbers space are space 80 space and space 20.
Q2. A theater charges Rs.70 for each evening show and Rs.50 for matinees. On one particular day, 1200 tickets were sold. Also, the number of people who watched evening shows on that day was 30 more than twice the number of people who watched matinee show. How many of each type of ticket did they sell and what is the money incurred from the evening shows?

Solution

Let the number of matinee tickets = x Number of tickets for evening show = 30 + 2x Total number of tickets = x + (30 + 2x) Given that the total number of tickets = 1200 x + (30 + 2x) = 1200 3x + 30 = 1200 3x = 1200 - 30 3x = 1170 x = 390 So number of tickets for the matinee show = 390 Number of tickets for the evening show = 30 + (2 × 390) = 30 + 780 = 810 Money incurred from the evening show = 810 × 70 = Rs.56700
Q3. The total cost of one shirt and one trouser is Rs. 1200. If the total cost of the trouser is double than the cost of shirt, find the cost of each.

Solution

Let space the space cost space of space one space shirt space be space Rs. space straight x. Then comma space the space cost space of space one space trouser space equals space Rs. space 2 straight x therefore space Total space cost space of space straight a space shirt space and space straight a space trouser equals Rs. space left parenthesis straight x plus 2 straight x right parenthesis equals Rs. space 3 straight x But space the space total space cost space is space given space as space Rs. space 1200. Thus comma space we space have 3 straight x equals 1200 rightwards double arrow straight x equals 1200 over 3 equals 400 rightwards double arrow 2 straight x equals 2 cross times 400 equals 800 Hence comma space the space cost space of space one space shirt space is space Rs. space 400 space and space the space cost space of space one space trouser space is space Rs. space 800.
Q4. Divide Rs. 1150 among Raju, Pappu and Minu such that the amount Raju receives is 5 times as much as Minu's share and is 3 times as much as Pappu's share.

Solution

Let space Minu apostrophe straight s space share space be space Rs. space straight x. Then comma space Raju apostrophe straight s space share equals Rs. space 5 straight x Hence comma space Pappu apostrophe straight s space share equals 1150 space minus space left parenthesis Raju apostrophe straight s space share space plus space Minu apostrophe straight s space share right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1150 space minus space left parenthesis 5 straight x space plus space straight x right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1150 space minus space 6 straight x It space is space given space that space Raju apostrophe straight s space share space is space 3 space times space Pappu apostrophe straight s space share. straight i. straight e. space 5 straight x equals 3 left parenthesis 1150 space minus space 6 straight x right parenthesis rightwards double arrow 5 straight x equals 3450 space minus space 18 straight x rightwards double arrow 5 straight x space plus space 18 straight x space equals space 3450 rightwards double arrow 23 straight x space equals space 3450 rightwards double arrow straight x equals 3450 over 23 equals 150 Thus comma space Minu apostrophe straight s space share equals Rs. space 150 space space space space space space space space space space space Raju apostrophe straight s space share equals Rs. space left parenthesis 5 cross times 150 right parenthesis equals Rs. space 750 space space space space space space space space space space space Pappu apostrophe straight s space share equals Rs. space left parenthesis 1150 space minus space 6 cross times 150 right parenthesis equals Rs. space 250
Q5. My age is five times the difference of my age after three years and my age three years back. What is my present age?

Solution

Let my present age be x years. Then, my age after 3 years = (x + 3) years And, my age 3 years back = (x - 3) years According to question, we have x = 5 [(x + 3) - (x - 3)] x = 5 [x + 3 - x + 3] x = 5 (6) x = 30 Hence, my present age is 30 years.


Comments

Post a Comment