RD Sharma Chapter 3: Pairs of Linear Equations in Two Variables Exercise 3.11 Solutions
If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle. Watch Solution
The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres. If the length is decreased by 7 metres and breadth is increased by 4 metres, the area is decreased by 21 sq. metres. Find the dimensions of the rectangle. Watch Solution
In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle. Watch Solution
The incomes of X and Y are in the ratio of 8 : 7 and their expenditures are in the ratio 19 : 16 . If each saves Rs 1250 , find their incomes. Watch Solution
A and B each has some money. If A gives Rs 30 to B, then B will have twice the money left with A. But, if B gives Rs 10 to A, then a will have thrice as much as is left with B. How much money does each have? Watch Solution
ABCD is a cyclic quadrilateral such that ∠A=(4y+20)°, ∠B=(3y−5)°, ∠C=(4x)° and ∠D=(7x+5)°. Find the four angles. Watch Solution
2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it? Watch Solution
In a △ABC, ∠A = x° ,∠B = (3x – 2)°, ∠C = y°.Also ∠C – ∠B = 9° .find the three angles .Watch Solution
In a cyclic quadrilateral ABCD, ∠A=(2x+4)° ,∠B=(y+3)° ,∠C=(2y+10)° , ∠D=(4x – 5)° Find the four angles. Watch Solution
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? Watch Solution
In a △ABC, ∠A = x°, ∠B = 3x° ,∠C=y°. If 3y – 5x = 30, prove that the triangle is right angled. Watch Solution
The car hire charges in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs 145 . What will a person have to pay for travelling a distance of 30 km ? Watch Solution
A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student a takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day. Watch Solution
Half the perimeter of a garden, whose length is 4 more than its width is 36 m. Find the dimensions of the garden. Watch Solution
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. Watch Solution
2 Women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by woman alone to finish the embroidery, and that taken by 1 man alone. Watch Solution
Meena went to a bank to withdraw Rs 2000 . She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many note Rs 50 and Rs 100 she received. Watch Solution
There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room. Watch Solution
A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327 . What is the basic first class full fare and what is the reservation charge? Watch Solution
A wizard having powers of mystic in candations and magical medicines seeing a cock, fight going on, spoke privately to both the owners of cocks. To one he said; if your bird wins, than you give me your stake-money, but if you do not win, I shall give you two third of that. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only 12 gold coins. Find the stake of money each of the cockowners have. Watch Solution
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of students in the class. Watch Solution
One says, “give me hundred, friend! I shall then become twice as rich as you” The other replies, “If you give me ten, I shall be six times as rich as you.” Tell me what is the amount of their respective capital? Watch Solution
A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs. 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs. 1028. Find the cost price of the saree and the list price (prince before discount) of the sweater. Watch Solution
In a competitive examination, one mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly? Watch Solution
A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for six days, while Anand paid Rs. 16 for the book kept for four days. Find the fixed charges and the charge for each extra day. Watch Solution
Pair of Linear Equations in Two Variables – R.D. Sharma Class 10th Math
