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Linear Equation In Two Variable

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Published in: Mathematics
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High order Thinking question on Linear Equation in two varianle

Sourabh J / Indore

10 years of teaching experience

Qualification: B.Sc

Teaches: Mental Maths, Mathematics, NSTSE, NTSE

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  1. LINEAR EQUATION IN TWO VARIABLES (Simultaneous linear equation in two variables) 1. If ax + by = c and bx + ay = d, Find the value of x2 —y . 2 2. Solve for x and y x—a y —b = 1 and c y—a a—b a c 3. Monica called a departmental store and ordered 4 pairs of black stockings and a few pair of blue stockings. The price of black stockings, per pair, was twice that of blue stockings. When her order arrived, she found out, that by mistake, the store personnel had interchanged the orders. As a result, the bill amount was half as much more a result, t e bill amount was half as much more again, as it should have been. How many blue stockings did she order? 4. Sum of the digits of a three digit numbers is 14 while its hundreds' digit is twice the tens' digit. If 72 is subtracted from the number, the digits change their places in forward cyclic order. Find the number. 5. A Civil engineer says that he can finish construction a particular section of highway in 2 months and 9 days, with his present supply f machines. However, if 6 more machines are given to him, he would finish the job 23 days earlier. How many machines does he have now? 6. A train overtakes two person completely, both of them going in the same direction as the train, at speeds 2kmph and 4kmph respectively. If the train takes 9 and 10 sec respectively to overtake them, find its length and normal speed in kmph. 7. A cyclist after travelling for some distance, stopped at a road side dhaabaa for lunch, Half an hour later, he went on a halbthe earlier speed , to complete his journey of 30 km. In total 5 hours. Had this d abaa been situated 10 Km further down the road , he would have been he would have saved an hour. Find his normal cycling speed and distance of the dhabaa from his starting point. 8 Station A is 40Km north of station B. Two cars starts from these stations, simultaneously. If they go towards south, the first car is still 16 Km behind the second, after 4hrs. But if they go in opposite directions, the distance between them, after 2 hours is 172 Km. Find their respective speeds. 9. Rs. 1300 is divided into two parts and invested at two different rates of interest per annum, the yearly interest on the first is Rs. 36 and on second is Rs. 49. However, If the two amounts are interchanged, the interest per annum, on both, would be same. Find the two rates of interest.
  2. 10. When two chemical solutions are mixed in ration 3:2 by volume, the density of the resulting mixture is 1.04gm per cm3, But it they are mixed in ratio 5:3, the density is 1.05g per cm3 Find the respective densities of the solutions. 11.A shopkeeper bought some tea mugs, at rate Rs. 40 per dozen and some glasses at rate Rs. 60 Per dozen, such that there were 24 glasses more than tea mugs. During transportation and handling 6 pieces were lightly damaged from each lot. He sold these damaged pieces cheaply at rate Rs. 24 per dozen for mugs and Rs. 36 per dozen for glasses. The rest of the mugs and glasses were earned a total profit of Rs. 122.50, on the whole transaction, how many mugs and glasses did he buy? 12.Karishma went to the Reliance fresh store and bought 3 bags of washing powder, 06 soap cakes a 5L jar of cooking oil, one Kg of mangoes and 2Kg of rice. The bill amounted to Rs. 634. Shaswati also went there, and bought same five items, She ought 4 bags of washing powder, 2Kg mangoes and 5Kg of rice. Since there wayan offer on sho cakes of 12 pieces for the price of 10 she bought 12 soap cakes, and also 2 jars of cookin oil. Her bill amount was more than Rs. 1000, So she got a 5% cash discount and thus final amount was Rs. 1102. 1 rd Ith If the price of soap cakes was - of that of 1 Kg of rice and of that of a bag of washing 3 5 powder, While the price of 1 Kg of cooking oil was Rs.4 less than that of 2Kg of mangoes. Find the price of each items. 13.A train starts from Gwalior at 5:00 AM and reaches New Delhi at 09:00AM another train starts from New Delhi at 07:00 ÅM and reaches Gwalior at 10:30 am At what time do the two trains cross each other. 14.Chayan and Ishaan, both greacricket fans were arguing about the outcome of a forthcoming one day series between ndia and ustralia. Chayan thought that India would win, while Ishaan was convinced o the opposite. Rituraj planned to take advantage of theirblind faiths. To chayan, he said ' If Indi"oes win, I will give you a certain sum of money, But in case India Losses, you have to give me 11/2 times of that amount". He betted some amount with Ishaan also, in same wav, against Australia's win, and in ratio 5:3 to his own benefit. Both of them wervso much confident of winning the bet, that they readily agreed to the best. Thus Rituraj was able to make a profit of Rs. 120, without any risk. How much money did he bet with either of them? 15.An old businessman had given big contracts to two ancillary manufacturers, but both were delaying their works. To motivate them, he proposed to the first, "If you complete your contract before the other guy, I will give you an extra 10% bonus on your cost. But if he beats you to it, I will deduct a 2000 penalty from your cost." To the second man he proposed in the same way, about the bonus and penalty of 15% and 25% respectively. As a result he was able to get both the jobs completed in record time, as well as save Rs. 70000 on the total project cost. How much was each contract worth?
  3. 16.Shankar, Ram and Mohan were very good friends. Shankar's and Ram's fathers gave them some money to invest, while Mohans' father could not give him any. Their friendship was so great that, both of them gave 25% of their respective capitals to Mohan to invest. Shankar invested his amount at 20% p.a. , Ram at 25% and Mohan at 24% together, they earned a total interest of Rs. 4650 in an year. If Shankar and Ram had interchanged their capitals, they would have earned Rs. 150 less. How much did Shankar and Ram get from their father to invest? 17.Amar , Akbar and Anthony travelled a total distance of 100Km, in the following way: Amar and Akbar set off on a scooter, at a speed of 25Kmph, at 08:30AM, While Anthony started walking at a speed of 5Kmph at same instant. After some time, Akbar got off the scooter and walked the remaining distance at 5Kmph, While Amar went back, picked up Ant ony and reached destination, simultaneously with Akbar. At what time did the reach there. 18.Sum of ages of Rajeshwar and Mahipal is 55years, WhepMahipal will be as old as Rajeshwar is now, sum of their ages would be 93 years. Find their present ages. 19.Ramlal said to his son mohan, "In 12 years, you will be as old as I was 12 years ago. But by then, I shall be thrice as old as you were 12 years ago." Find their present ages. 20. Vishwanath said to Ramnath, "I am 5 times as old as you were, when I was as old as you are.' If the sum of their present age is 64 years, Find their present ages. 21 .Sum of the ages of Manohar, and his father, Devilal is 102 years, When Manohar will be as old as his father is now, he will also be eight times as old as his son, Rohan is now. Rohan will be four years younger than Manohar i now, When Manohar will be as old as his father is now. Find their present ages. 22.Mr. Ashok Sharma isc6 years older than his wife, Mrs. Aasha, who was 18 years old when her elder son, Abhishek was born.2Today, Mr. Ashok's age is 10 years more than twice the age of their second son, Abhijeet.While Mrs. Aasha's age is 10 years less than thrice the age of their youngest daughter Amisha. Abhisheks' wife, Aishvarya is 3 years older than Amisha, and 1/3rd as 01 as, the grandmother, Mrs. Artidevi was 7 years ago. If, today Artidevi's age is 8 ears less than thrice Abhishek's age, Find the present ages of all members of Sharma family. ca..e

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