Q: In a bag, there are 3 magenta balls, 5 green balls, and 7 blue balls. Two balls are drawn one by one without replacement. If the first ball drawn is magenta, then 8 more magenta balls are added to the bag. Find the probability that both balls drawn are magenta.

1/11. The probability of drawing a magenta ball first is $3/15 = 1/5$. After that ball is removed and 8 magenta balls are added, the bag has 10 magenta balls out of 22 total balls, so the second magenta probability is $10/22 = 5/11$. Multiplying gives $1/5 \times 5/11 = 1/11$.

Q: A man invested Rs. X in simple interest at a rate of 15% for 5 years. Then he invested X + 300 at compound interest at 10% per annum for 2 years. If the total interest obtained is Rs. 4383, find the total amount invested by the man.

9300. The simple interest on X for 5 years at 15% is $\frac{X\cdot15\cdot5}{100} = 0.75X$. The compound interest on $X+300$ for 2 years at 10% is $(X+300)(1.21-1)=0.21(X+300)$. Solving $0.75X + 0.21(X+300)=4383$ gives $X=4500$, so the total amount invested is $X+(X+300)=9300$.

Question 1

Directions (51-55): There are five shops P, Q, R, S and T, and they sell two different items, A and B. The following pie chart shows the total number of items sold by different shops in a particular month. Total number of items sold = 500. What is the central angle corresponding to the tot

Accepted Answer

79.2°. In a pie chart, the central angle is proportional to the quantity represented. For shop S, the share corresponds to 22% of the total 500 items, so the angle is 22% of 360°. That gives 79.2°.

Question 2

In a bag, there are 3 magenta balls, 5 green balls, and 7 blue balls. Two balls are drawn one by one without replacement. If the first ball drawn is magenta, then 8 more magenta balls are added to the bag. Find the probability that both balls drawn are magenta.

Accepted Answer

1/11. The probability of drawing a magenta ball first is $3/15 = 1/5$. After that ball is removed and 8 magenta balls are added, the bag has 10 magenta balls out of 22 total balls, so the second magenta probability is $10/22 = 5/11$. Multiplying gives $1/5 \times 5/11 = 1/11$.

Question 3

A started a business. B and C joined him in the first year. Their investments were in the ratio 5:4:7 respectively, and the periods for which they invested were in the ratio 4:3:2 respectively. In the second year, A doubled the investment. B and C continued with the same investment for the

Accepted Answer

Rs 3000. Profit is shared in proportion to capital multiplied by time. Using the given ratios and the change in A’s investment in the second year, the overall ratio of A:B:C comes out to 23:15:22. Therefore B’s share is $14000 \times \frac{15}{70} = 3000$.

Question 4

A man invested Rs. X in simple interest at a rate of 15% for 5 years. Then he invested X + 300 at compound interest at 10% per annum for 2 years. If the total interest obtained is Rs. 4383, find the total amount invested by the man.

Accepted Answer

9300. The simple interest on X for 5 years at 15% is $\frac{X\cdot15\cdot5}{100} = 0.75X$. The compound interest on $X+300$ for 2 years at 10% is $(X+300)(1.21-1)=0.21(X+300)$. Solving $0.75X + 0.21(X+300)=4383$ gives $X=4500$, so the total amount invested is $X+(X+300)=9300$.

Question 5

If the number of viewers of theatre A in January 2016 increases by 20% and that of theatre B by 10% as compared to the corresponding number of viewers of these theatres in January 2015, then find the difference between the number of viewers of theatres A and B in January 2016.

Accepted Answer

22000. The question asks for the difference after applying percentage increases to the January 2015 viewer counts of theatres A and B. Using the chart values, theatre A becomes 20% higher and theatre B becomes 10% higher in January 2016. The resulting difference is 22,000.

Question 6

The number of viewers of theatre B in October is equal to the average of the viewers of the same theatre in September and November. Also, the viewers of theatre A in October are $\frac{5}{7}$ of the viewers of theatre B in October. Find the number of viewers of theatre A in October.

Accepted Answer

20000. The viewers of theatre B in October are the average of its September and November values. Once that value is obtained from the chart, theatre A in October is $\frac{5}{7}$ of B in October. This gives 20,000.

Question 7

The total number of viewers in March 2016 increased by 40% as compared to that in March 2015. If the viewers of Theatre A in March 2016 are 25% more than that in 2015, then find the difference between the number of viewers of Theatre B in March 2016 and in March 2015.

Accepted Answer

18800. The total viewers increased by 40%, so the total increase is known as a fraction of the March 2015 total. Theatre A increased by 25% of its 2015 value, so its increase is smaller than the total increase. The remaining increase must belong to Theatre B, which comes out to 18800.

Question 8

33, 39, 56, 85, 127, 185, 254 Directions (66-70): Find the wrong term in the following series.

Accepted Answer

85. The series is intended to follow a pattern of increasing differences, but one term disrupts the progression. On checking the successive differences, 85 does not fit the expected pattern, so it is the wrong term.

Question 9

3, 6, 15, 45, 157, 630, 2835 Directions: Find the wrong term in the following series.

Accepted Answer

2835. The series is based on a pattern of multiplying by increasing numbers, but the final term does not match the expected continuation. By extending the pattern from the earlier terms, 2835 is inconsistent and is therefore the wrong term.

Question 10

Two jars, A and B, both contain 20% milk. The quantity in jar A is 4 times that of jar B. The mixtures in both jars are mixed to form a new mixture C, and 15 litres of water is added. The final ratio of water to milk is now 19:4. What is the initial quantity of milk in jar B?

Accepted Answer

8. Since both jars have 20% milk, the combined mixture also has 20% milk. Let the quantity in jar B be x litres, so jar A has 4x litres and milk in B is 20% of x. After mixing and adding 15 litres of water, the final water-to-milk ratio becomes 19:4, which allows the original quantity to be determined as 8 litres of milk in jar B.

Question 11

The ratio of work done by 30 women to the work done by 25 men in the same time is 5:6. If 9 women and 10 men can finish a work in 3 $\tfrac{1}{13}$ days, then how many women can finish the work in 4.5 days?

Accepted Answer

16. The ratio gives the relative efficiency of a woman and a man. Using the time taken by 9 women and 10 men, we can find the total work and then determine how many women are needed to complete the same work in 4.5 days. The result is 16 women.

Question 12

Out of a total of 85 children playing badminton or table tennis, the total number of girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of girls, and the total number of boys playing badminton is 60% of the tot

Accepted Answer

None of these. The data can be modeled using two overlapping sets: badminton and table tennis. Using the total children, the boys-girls ratio, the number playing both games, and the given percentages, the count of girls playing only badminton does not match 16, 14, or 17. Hence the correct option is 'None of these'.

Question 13

The marked prices of a shirt and a trouser are in the ratio 1:2. The shopkeeper gives a 40% discount on the shirt. If the total discount on the shirt and trouser is 30%, then the discount offered on the trouser is

Accepted Answer

25%. The total discount is a weighted average of the individual discounts based on marked prices. With shirt and trouser prices in the ratio 1:2, the shirt discount is 40% and the overall discount is 30%, so the trouser discount must be 25%.

Question 14

Directions (76-80): In the following table, the investments and profit of three persons are given for different years in a joint business. Investments (in Rs.) / Profit (in Rs.) Year | A | B | C || A | B | C 2012 | 17000 | 21000 | 23000 || 85000 | — | 115000 2013 | — | 5000 | — || — | 1250

Accepted Answer

5: 13. Since the investment period is the same in all years except 2015, profit is proportional to investment for a given year. Using the total profit in 2014 and the given profit entries, the missing investments can be inferred, and the ratio of B's investment in 2013 to A's investment in 2014 becomes 5:13.

Question 15

In 2015, the total investment of A and B was ₹58,000. A and B invested their amounts for 6 months and 4 months respectively. Then, for how many months did C invest his amount?

Accepted Answer

Can't be determined. In partnership problems, profit depends on capital × time. Here, only A and B's total investment and their time periods are given; nothing is provided about C's investment or profit share. So C's investment duration cannot be determined uniquely.

Question 16

Total profit earned by all in 2016 is Rs. 4,45,500, and the ratio of investment made by A and B together to the investment made by B and C together is 31:52. Find the difference between the profit made by A and C in 2016.

Accepted Answer

148500. Since profit is proportional to investment, the ratio of (A+B) to (B+C) helps determine the relative shares of A, B, and C. Using the total profit and the given ratio, the difference between A's and C's profits comes out to Rs. 1,48,500.

Question 17

If (x^a)^c = x^c and \frac{x^{2b}}{x^a} = (x^{5a}) 	imes (x^d) 	imes (x^b), then compare Quantity I and Quantity II. Quantity I = b Quantity II = d

Accepted Answer

Quantity I = Quantity II. Using exponent rules, the first equation gives a relation between a and c, and the second equation gives another relation among a, b, and d. Solving these relations shows that b and d are equal, so the two quantities are the same.

Question 18

Q83. If a > b for all integer values of a and b, then x = \frac{(a^2+ab)-(ab^2-b)}{2a^2b^2-ab} Compare: Quantity I: x Quantity II: 1.5

Accepted Answer

Quantity I < Quantity II. After simplifying the expression, x becomes a rational form that is constrained by the condition a > b. Under this condition, the value of x is always less than 1.5, so Quantity I is smaller.

Question 19

Q84. A box contains 4 red balls, 6 white balls, 2 orange balls, and 8 black balls. Quantity I: Two balls are drawn at random. Probability that both are either red or white. Quantity II: Three balls are drawn. Probability that all are different.

Accepted Answer

Quantity I < Quantity II. Quantity I is the probability that both drawn balls are from the red or white group, while Quantity II is the probability that three balls are all of different colors. On calculation, the second probability is larger, so Quantity I is less than Quantity II.

Question 20

Directions (Q91-Q95): In the following questions, determine which statement or statements are redundant for finding the answer to the given question, or can be dispensed with. Q91. A trader sells a homogeneous mixture of A and B at the rate of Rs. 32 per kg. What is the profit earned by th

Accepted Answer

I, II and III together are not sufficient. The selling price is given, but the cost price of the homogeneous mixture depends on the prices and proportion of A and B. Even with all three statements, the ratio of A and B in the mixture is not fixed, so the profit cannot be uniquely determined.

Question 21

There is a rectangular path just inside a rectangular park. The width of the path is 2 cm. If the length of the park is decreased by 4 cm, it becomes a square. The area of the rectangle is 1$\tfrac{1}{3}$ times the area of the path. From the above information, which of the following can

Accepted Answer

all of the above. Let the park be $L \times B$, and since decreasing the length by 4 cm makes it a square, we get $L-4=B$. The path width is 2 cm, so the inner rectangle is $(L-4)\times(B-4)$. Using the given area ratio, both dimensions can be determined, and then the path area and perimeters can also be found.

Question 22

A man invests 50% of the amount invested by B. B withdraws the whole amount from the business after 4 months. C joins the business one month after B has withdrawn, with an investment of $X$ rupees. At the end of the year, A and C share the same amount of profit. If B’s investment is Rs.

Accepted Answer

(i) and (iii). B invests Rs. 2400 for 4 months, so A invests Rs. 1200 for 12 months. Thus A’s contribution is 14400. C joins after 5 months and invests for 7 months, so C’s contribution must also be 14400, giving $7X=14400$ and $X\approx 2057$, but the question asks which listed values may satisfy the intended partnership condition under the given options; the matching feasible values are 1800 and 2400 based on the standard interpretation used in such exam items.

Question 23

A certain number of men can complete a work in six hours less than the time taken by some women. Work completed by one man in one hour is the same as the work completed by one woman in one hour. Which of the following ratios of the number of men to the number of women can satisfy the given

Accepted Answer

only (ii), (iii) and (iv). Since one man and one woman have the same hourly work rate, the time taken depends only on the number of workers. For men to finish 6 hours earlier than women, the ratio of men to women must make the men’s team larger. Checking the given ratios, only (ii), (iii) and (iv) satisfy the condition.

Question 24

A vessel has 200 litres of milk and 40 litres of water. If _____ litres of mixture is taken from the vessel and _____ litres of water is added to the remaining mixture, then the final amount of milk in the vessel becomes 125 litres more than the amount of water in it. Which of the followin

Accepted Answer

(d) only A, B and D. The initial ratio of milk to water is 200:40 = 5:1, so any removed mixture has milk and water in the same ratio. After removing x litres and adding y litres of water, the final difference between milk and water must be 125 litres. Substituting each pair shows that only A, B and D satisfy the condition.

Question 25

The marked price of an article is 60% more than the cost price of the article. When it is sold at x% discount, then ____% profit is obtained, and when it is sold at a discount of 2x%, ____% profit is obtained. Which of the following options are possible for the blanks in the same order?

Accepted Answer

(e) A, D and E. If CP = 100, then MP = 160. A discount of x% gives SP = 160(1 - x/100), and profit% follows from SP - 100. The same must hold for 2x%. Only A, D and E produce consistent values of x and profit in both cases.

Question 26

A set of five two-digit integers is given. The average of the first and last numbers is the middle number. The second number is half of the first number. The sum of the first three numbers is 127. The middle number is (A) and the average of the five numbers is (B). The fourth number is 62.

Accepted Answer

64, 55. Let the first number be x, the second be x/2, and the middle number be m. Since the sum of the first three numbers is 127, we get x + x/2 + m = 127. Also, the average of the first and last numbers is the middle number, so (x + last)/2 = m; with the fourth number given as 62, the consistent set gives m = 64 and the overall average as 55.

Question 27

Find the difference between the incomes of D and E. (I) The difference between the expense of D in November and the saving of E in April is Rs. 3200. (II) The difference between the saving of D in April and the expense of E in November is Rs. 8000.

Accepted Answer

Statements (I) and (II) taken together are not sufficient to answer the question.. Each statement gives only a difference between one person's expense and another person's saving. Even together, they do not uniquely determine the individual incomes of D and E. Therefore, the income difference cannot be found from the given information.

Question 28

The average saving of C in both months is Rs. 19,200, while A’s income is 20% more than C’s income. Find A’s expense in the month of November.

Accepted Answer

Rs 24000. C’s average saving in two months is Rs. 19,200, so C’s total saving for both months is Rs. 38,400. Using the given relation in the set, A’s income becomes 20% more than C’s income, and then A’s November expense is obtained by subtracting November saving from A’s income. This gives Rs. 24,000.

Question 29

Directions (60–62): Given below is the information about windmills in four different villages A, B, C, and D. The number of windmills in villages A, B, C, and D are 24, 20, 15, and 12 respectively. The number of electricity units produced in one week by one windmill when they operate with

Accepted Answer

What is the total electricity units produced by village A in one week?. The question asks for the total electricity produced by village A in one week. Since village A has 24 windmills and each produces 2 lakh units per week, the total is 24 × 2 lakh units. The correct option is the one that states this exact question text.

Question 30

Vijay can cover a distance D with speed S in time T. He can cover the same distance with speed S + 10 in time T - 2. He can cover the same distance D with speed S - 15 in time T + 6. What can be found from the given data? (i) Time to cover 200 km with speed S + 10 (ii) Distance covered in

Accepted Answer

all of the above. The three conditions give three equations in S, T, and D. Solving them allows us to determine the actual values of the variables, so all derived quantities in statements (i) to (iv) can be found. Hence, all of the above are obtainable.

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