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Pair of Linear Equations in Two Variables

Short Answer Type

21. Students of class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the number of students in the class.

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22. A person invested some amount at the rate of 12% simple interest and the remaining at 10%. He received yearly interest of Rs. 130 but if he had interchanged the amounts invested he would have received Rs. 4 more interest. How much money did he invest at different rates.

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23. There are two class room A and B. If 10 students are sent from A to B, the number of students in each room becomes the same. If 20 students are sent from B to A, the number of students in A becomes double the number of students in B. Find the number of students in each class room.

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24. On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea set at 5% gain and lemon set at 10% gain, he gains Rs. 13. Find the actual price of the tea set and lemon set.

Solution not provided.
Ans. 100, 80

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25. A takes 3 hours more than B to walk a distance of 30 km. But, if A doubles his pace (speed), he is ahead of B by 1/2 hours. Find their speeds of walking.

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26. In a bag containing only white and black balls, half the number of white balls is equal to one third ol the number of black balls. Two times the total number of balls exceeds three times the number of black balls by 4. Find number of balls of each type in the bag.

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27. Solve for x and y : 147x - 231y = 525; 77x - 49y = 203.

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28. After covering a distance of 30 km with a uniform speed there is some defect in a railway engine and therefore its speed is reduced to 4/5th of this original speed. Consequently the train reaches its destination late by 45 minutes. Had it happened after covering 18 km more, the train would have reaches 9 minutes earlier. Find the speed of the train and the distance of journey.

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