**Directions (1-5): The following questions are accompanied by two statements I and II. You have to determine which statements(s) is/are sufficient/necessary to answer the questions. **

(a) Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions.

(b) Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question

(c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

(d) Either statement I or statement II by itself is sufficient to answer the question.

(e) Statements I and II taken together are not sufficient to answer the question.

**Q1. How much % B is less efficient than A? **

(i) If A only works for 7 days with B then the remaining work is completed by B in 8 more days then time taken by them is 5 days longer than if they had worked together.

(ii) time taken by B alone to complete 45% of work is 4 days less than the time taken by A alone to complete whole work.

**Q2. A and B are standing on opposite ends of a road. What is difference in their speed (in km/hr). **

(i) Ratio of their running speed is 2: 3 and time taken by each of them to cross whole road by running is 7.5a hours & 5b hours, where a and b are equal coefficients.

(ii) Length of road is 150 km. After they had started running, both of them after reaching their opposite end points, they start running back to their initial point and meet again after 9 hours from the time they had initially started race.

**Q3. Let x be total number of balls in a bag. Balls are of three different colors of black, white and red. Calculate (x-1). **

(i) Probability of getting a black ball is ⅙, a red ball is ⅙ & a white ball is ⅔.

(ii) If one white ball is lost, probability of not getting a white ball is 8/23 and initial number of white balls in bag is less than 27.

**Q4. Raj and Simran invested in a business in the ratio of 5 : 7. What is the profit share of Simran. **

(i) Simran invested Rs. 35000/- and Raj invested for 12 months & Simran for 9 months and 2% of Raj’s Profit is Rs. 1600.

(ii) Time for which they invested is in the ratio of 4 : 3 and Raj got Rs. 4000 less than Simran as profit share.

**Q5. Calculate the cost price of item? **

(i) The profit earn on item is 33⅓% and MP of item is Rs 4 less than twice of its SP.

(ii) Discount given on item is Rs 28.

**Solutions**