2. | There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is: | |||||||
Answer: Option C Explanation:
Let the number of students in rooms A and B be x and y respectively. Then, x – 10 = y + 10 x – y = 20 …. (i) and x + 20 = 2(y – 20) x – 2y = -60 …. (ii) Solving (i) and (ii) we get: x = 100 , y = 80. The required answer A = 100. |
3. | The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: | ||||||||||||||||||||||
Answer: Option D Explanation:
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
15x + 2y = 4000
20x = 4000 x = 200.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Rs. (2400 + 1500) = Rs. 3900. |
4. | If a – b = 3 and a^{2} + b^{2} = 29, find the value of ab. | |||||||
Answer: Option A Explanation:
2ab = (a^{2} + b^{2}) – (a – b)^{2} = 29 – 9 = 20 ab = 10. |
5. | The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | |||||||||
Answer: Option B Explanation:
Let the price of a saree and a shirt be Rs. x and Rs. y respectively. Then, 2x + 4y = 1600 …. (i) and x + 6y = 1600 …. (ii) Divide equation (i) by 2, we get the below equation. => x + 2y = 800. --- (iii) Now subtract (iii) from (ii) x + 6y = 1600 (-) x + 2y = 800 ---------------- 4y = 800 ---------------- Therefore, y = 200. Now apply value of y in (iii) => x + 2 x 200 = 800 => x + 400 = 800 Therefore x = 400 Solving (i) and (ii) we get x = 400, y = 200. Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400. |