Monday 21 June 2021

ages sums quadratic equations


Ages

1.Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.

2.The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.

3.The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.

4.The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.

5.Find the percent age of a man if his age 40 years hence will become equal to the square of what his age was 32 years ago.

6.Mrs Tendon has two sons, one being exactly one year older than the other. At percentage, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the percent ages of her sons.

7.zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?

8.The product of the ages of Sally and Joey now is 175 more than the product of their ages 5 years prior. If Sally is 20 years older than Joey, what are their current ages?

9.The product of the ages of Alan and Terry is 80 more than the product of their ages 4 years prior. If Alan is 4 years older than Terry, what are their current ages?

10.The product of the ages of Cally and Katy is 130 less than the product of their ages in 5 years. If Cally is 3 years older than Katy, what are their current ages?

11.The product of the ages of James and Susan in 5 years is 230 more than the product of their ages today. What are their ages if James is one year older than Susan?

12.he product of the ages (in days) of two newborn babies Simran and Jessie in two days will be 48 more than the product of their ages today. How old are the babies if Jessie is 2 days older than Simran?

13.The sum of the age of a man and his son is 35 years and the product of their ages is 150. Find their ages.


14.The product of the man’s age 5 years ago and 5 years later is 600. Find his present age.

15.year ago a father was 8 times as old as his son. Now his age is square of his son’s age. Find the present age.

16.Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

17.Ten years from now, Orlando will be three times older than he is today. What is his current age?

I18.n 20 years, Kayleen will be four times older than she is today. What is her current age?

19.Phil is Tom's father. Phil is 35 years old. Three years ago, Phil was four times as old as his son was then. How old is Tom now?


20.Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa?


21.Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

22.The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

23.A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

24.A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

25.Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

.26. Father is four times the age of his daughter. If after 5 years, he would be threee times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?


26.What is Aman's present age, if after 20 years his age will be 10 times his age 10 years back?


27.Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

28.One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?

29. Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages

. 30.Saransh is 50 years old and Nazma is 40 years old. How long ago was the ratio of their ages 3:2?

31.The ratio of the present ages of Pranav and Qureshi is 4:5. Five years ago, the ratio of their ages was 7:9. Find their present ages? (In years)

 32.man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.

33.Dinesh is younger to Roshan by 9 years. If their ages are in the respective ratio of 4:5, how old is Dinesh?


34.The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1: 1. Presently, the ratio of their ages is 5: 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.


35.Ashu is x years old while his mother Mrs. Veena is x2 years old. Five years hence Mrs. Veena will be three times old as Ashu. Find their present ages. 

35.The sum of the ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man’s age at the time. Find their present ages.

35.The product of Shikha’s age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

36.The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu’s present age. 


digit sums quadratic equations 10th

The product of the digits of a two-digit number is 12. If 36 is added to the number, a number is obtained which is the same as the number obtained by reversing the digits of the original number.

two-digit number is made of two consecutive digits such that the sum of their squares is 4 less than the number. Find the two-digit number.

two digit number is such that the product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places.

AA two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.

A two digit number is four times the sum and 3 times the product of its digits, find the number.

A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.

A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.

A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.

 two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the number.

A two digit number is such that the product of its digits is 12. When 36 is added to this number the digits are interchanged. Find the numbers.

the digits of a two-digit number are interchanged, the number so formed is 18 more than the original number. The sum of digits is 8. What is the thrice value of original number?

two-digit number is eight times the sum of its digits. If 45 is subtracted from the numbers, the position of digits get interchanged. The number is:

The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.

The sum of two digits of a 2-digit number is 13. Reversing the digits increase the number by 45. What is the number?

The sum of the digits of a two digit number is 9. When the digits are reversed the new number is 9 less than three times the original.

The sum of the digits of a 2-digit number is 10. The tens digit is 4 times the ones digit. Find the number.

2. A 2-digit number is 10 times the sum of its digits. The tens digit is 2 greater than the units digit. Find the number.

3. The sum of the digits of a 2-digit number is 14. If 18 is added to the number, the result is the number with its digits reversed. Find the original number.

4. The sum of the digits of a 2 digit number is 9. If the digits are reversed, the new number is 9 less than 3 times the original number. Find the original number.

One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

The sum of the digits in a two digit number is seven. If the tens
digit is three less than the ones digit, find the number.

The sum of the digits in a two digit is thirteen. If the digits of the
number are reversed, the new number is nine more than the original number.
What is the original number?

The sum of the digits in a two digit number is sixteen. If the tens digit is two less than the ones digit, find the number.

In a three digit number, the hundreds digit is three times the tens
digit. The tens digit is three times the ones digit. If the sum of the digits is
thirteen, find the number.

The sum of the digits in a two digit number is fifteen. If the tens
digit is three less than the ones digit, find the number.

The sum of the digits in a two digit is thirteen. If the digits of
the number are reversed, the new number is twenty-seven less than the original
number. What is the original number?

The sum of the digits in a two digit number is 8. If the tens digit is
three times the ones digit, find the number.

) In a three digit number, the hundreds digit is one half of the tens
digit. The tens digit is twice the ones digit. If the sum of the digits is eight, find the
number.

The sum of the digits in a two digit number is seven. If the tens
digit is five less than the ones digit, find the number.

The sum of the digits in a two digit is fourteen. If the digits of the
number are reversed, the new number is thirty-six more than the original
number. What is the original number?

The sum of the digits in a two digit number is nine. If the tens
digit is seven less than the ones digit, find the number.

In a three digit number, the hundreds digit is two more than the
tens digit. The tens digit is three more than the ones digit. If the sum of the digits
is fourteen, find the number.

The sum of the digits in a two digit number is twelve. If the tens
digit is four more than the ones digit, find the number.

The sum of the digits in a two digit is three. If the digits of the
number are reversed, the new number is nine less than the original number.
What is the original number?

The sum of the digits in a two digit number is fifteen. If the tens
digit is one more than the ones digit, find the number.

In a three digit number, the hundreds digit is two less than the
tens digit. The ones digit is six more than the tens digit. If the sum of the digits is

The sum of the digits in a two digit number is six. If the tens
digit is two more than the ones digit, find the number.

) The sum of the digits in a two digit number is nine. If the tens
digit is five more than the ones digit, find the number.

The sum of the digits in a two digit number is eleven. If the
tens digit is three less than the ones digit, find the number.

In a three digit number, the hundreds digit is two more than
the tens digit. The ones digit is two less than the tens digit. If the sum of the digits
is twenty-one, find the number.

A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.

A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. Determine the number.

two-digit number is such that the product of the digits is 16. When 54 is subtracted from the number, the digits are interchanged. Find the number.

two digit number is 4 times the sum of its digits and twice the product of its digits. Find the digits



Saturday 19 June 2021

work and time sums quadratice equations 10th cbse

Ram takes 5 days less than Bhagat to finish a piece of work. If both of them together can finish the work in 4 days, in how many days Bhagat alone can finish the work ?

A takes 5 days less than the time taken by B to finish a piece of work. If both A and' B together can finish it in 4 days, find the time taken by B to finish the work.

A and B working together can do a work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can do it alone

a takes 16 days less than the time taken by b to finish a piece of work if both A and B together can finish it in 6 days find the time taken by b to finish the work

Saturday 12 June 2021

speed sums ,picnic sums , cost sums, quadratic equations

Speed sums same as other sums

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.

 fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.

A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.

The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction ?

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.

train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete^total journey, what is its original average speed?

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speeds of the two trains.


An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hr. Find the original speed / hour of the plane.

A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/ hour. Find the time taken to cover the distance.

1.piece of cloth costs Rs. 35. If the piece were 4 m longer and each metre costs Re. one less, the cost would remain unchanged. How long is the piece 

2.Some students planned a picnic. The budget for food was Rs. 480. But eight of these failed to go and thus the cost of food for each member increased by Rs. 10. How many students attended the picnic ?

3.If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys mope for Rs. 360. Find the original price of the toy.

4.Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

5.Some students planned a picnic. The budget for food was Rs. 500. But 5 of them failed to go and thus the cost of food for each number increased by Rs. 5. How many students attended the picnic?

6.In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of their marks, would have been 180. Find his marks in the two subjects.

7.In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in two subjects.

8.
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90, And the number of articles produced and the cost of each article.

9.At t minutes past 2 pm the time needed by the minutes hand and a clock to show 3 pm was found to be 3 minutes less than t24 minutes. Find t.

10.piece of cloth costs RS.75. If the piece were 4 metre longer and each metre costs RS.5 less, the total cost would remain unchanged. How long is the piece?

11.The total cost of a certain length of a piece of wire is Rs. 200. If the piece was 5 metres longer and each metre of wire costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre?

11.A lady purchased one piece of cloth for Rs 1600 .Had the price rate of cloth been Rs 40 per metre less,then she would have purchase 2 metre cloth more in the same amount.Find the measure of cloth and price per metre.

12.a piece of cloth costs Rs.300.If the piece was 5 metre longer and each metre of cloth costs Rs.2 less, the cost of the piece would have remained unchange.How long is the original piece of cloth and what is the rate per metre?

13.Some students planned a picnic and budget for food was USD 500. But, 5 of them failed to go and thus the cost of food for each member increased by USD 5. How many students attended the picnic?

14.Some students planned a picnic. The budget for food was Rs.500. But 5 of them failed to go and thus the cost of food for each member increased by Rs.5. How many students attend the picnic?


15.Some students planned a picnic. the total budget for food was rupees 2000 but 5 student failed to attend the picnic and thus the cost of food for each member increased by rupees 20 how

16.Some students planned a picnic. The total budget for hiring a bus was Rs. 1440. Later on, eight of these refused to go and instead paid their total share of money towards the fee of one economically weaker student of their class, and thus, the cost for each member who went for picnic, increased by Rs. 30.How many students attended the picnic?How much money in total was paid towards the fee? Which value is reflected in this question?

17.class decided to have a party at a total cost of Rs 720. Four students decided to stay out of the party. To meet the expenses the remaining students had to increase their share by Rs 9. What is the original cost per student?

18.There were 35 students in a hostel. If the number of the students is increased by 7, then the expenses of the mess increase by Rs 42 per day, while the average expenditure per head diminishes by Rs 1. The original expenditure of the mess per day was

19.some students planned a picnic. the total budget for hiring a bus was Rs1440.Later on 8 of these refused to go and instead paid their total share of money towards the fee of one ecnomically weaker student of their class,and thus the cost of each member who went for the picnic increased by Rs30.
)how many students attended the picnic.2)how much money in total was paid towards the fee

20.
some students arranged a picnic. the budget for food was Rs240. Because four students of the group failed to go, the cost of rach student got increased by Rs5. how many students went for picnic

21.some students planned a picnic.The budget for food was rs 960. But four of them failed to go and thus the cost of food for each friend increased by rs 12. How many friends went to the picnic