Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
What will come in place of the question mark (?) in the following number series?
1, 3, 8, 19, 39, 71, ?
128
228
118
108
None of these
Correct answer
118
Why this answer is correct
Pattern of the given series can be explained as,
What will come in place of question mark (?) in the following number series?
10, 15, 25, 40, ?, 85
55
65
50
70
60
Correct answer
60
Why this answer is correct
Given:
The number series:
10, 15, 25, 40, ?, 85
Concept Used:
Number series following a fixed pattern.
Calculation;
The given number series follows the pattern:
10 + (5 × 1) = 15
15 + (5 × 2) = 25
25 + (5 × 3) = 40
40 + (5 × 4) = 60
60 + (5 × 5) = 85
∴ The number in place of “?” in the given number series is 60
What will come in place of question mark (?) in the following number series?
12, 13, 28, ?, 352, 1765
102
81
91
87
105
Correct answer
87
Why this answer is correct
Given:
The number series:
12, 13, 28, ?, 352, 1765
Concept Used:
Number series following a fixed pattern.
Calculation;
The given number series follows the pattern:
12 × 1 + 1 = 13
13 × 2 + 2 = 28
28 × 3 + 3 = 87
87 × 4 + 4 = 352
352 × 5 + 5 = 1765
∴ The number in place of “?” in the given number series is 87
What will come in place of question mark (?) in the following number series?
10, 11, 15, 24, ?, 65
42
45
48
35
40
Correct answer
40
Why this answer is correct
Given:
The number series:
10, 11, 15, 24, ?, 65
Concept Used:
Number series following a fixed pattern.
Calculation;
The given number series follows the pattern:
10 + 12 = 11
11 + 22 = 15
15 + 32 = 24
24 + 42 = 40
40 + 52 = 65
∴ The number in place of “?” in the given number series is 40
What should come in place of question mark ‘?’ in the following number series?
27, 38, 51, 68, 87, ?
100
120
115
110
None of these
Correct answer
110
Why this answer is correct
Given:
27, 38, 51, 68, 87, ?
Calculation:
The series follows the following pattern
27 + 11 = 38
38 + 13 = 51
51 + 17 = 68
68 + 19 = 87
87 + 23 = 110
∴ The Required term in the series will be 110
Speed of Suraj is 16 km/h in still water. Current is flowing at the rate of 4 km/hour, what will be the average speed (in km/h) of Suraj in the journey comprising of an upstream and a downstream journey.
15
20
25
22
18
Correct answer
15
Why this answer is correct
Shortcut Trick
Speed in still water (u) = 16 km/h, Speed of current (v) = 4 km/h.
Downstream speed (D) = u + v = 16 + 4 = 20 km/h.
Upstream speed (U) = u − v = 16 − 4 = 12 km/h.
Average Speed for a round trip = [2 × D × U] ÷ [D + U] = [2 × 20 × 12] ÷ [20 + 12] = 480 ÷ 32 = 15 km/h.
∴ The correct answer is 15 km/h.
Alternate Method
Given:
Speed of Suraj in still water (u) = 16 km/h
Speed of current (v) = 4 km/h
Formula Used:
Downstream Speed = u + v
Upstream Speed = u − v
Average Speed = (Total Distance) ÷ (Total Time)
Calculations:
⇒ Downstream Speed (D) = 16 + 4 = 20 km/h
⇒ Upstream Speed (U) = 16 − 4 = 12 km/h
⇒ Let the distance for one way be 'd' km.
⇒ Total distance = d + d = 2d
⇒ Total time = (d ÷ 20) + (d ÷ 12) = (3d + 5d) ÷ 60 = 8d ÷ 60
⇒ Average speed = 2d ÷ (8d ÷ 60) = (2d × 60) ÷ 8d = 120 ÷ 8
⇒ Average speed = 15 km/h
∴ The correct answer is 15 km/h.
Additional Information
Downstream and Upstream Speed
Downstream speed is the sum of speed in still water and stream speed (u+v), while upstream is the difference (u−v).
Average Speed for Constant Distance
When distances are equal, Average Speed = (2 × x × y) ÷ (x + y), where x and y are the speeds for the two parts.
Speed in Still Water from D and U
Speed in still water (u) = (Downstream speed + Upstream speed) ÷ 2.
Current Speed from D and U
Current speed (v) = (Downstream speed − Upstream speed) ÷ 2.
Pavan is 12 years older than Raghav and the respective ratio of Raghav's age 8 years hence and Shreya's present age is 17 : 7. If at present Pavan's age is thrice the age of Shreya. What will be Pavan's age 3 years hence?
21 yrs
24 yrs
27 yrs
25 yrs
22 yrs
Correct answer
24 yrs
Why this answer is correct
Shortcut Trick
Let Shreya's present age be 7 units based on the given ratio.
Then, Raghav's age 8 years hence = 17 units.
Pavan's present age = 3 × Shreya = 21 units.
Difference between Pavan and Raghav: (21 units) − (17 units − 8) = 12 years.
⇒ 4 units + 8 = 12 ⇒ 4 units = 4 ⇒ 1 unit = 1 year.
Pavan's present age = 21 × 1 = 21 years.
Pavan's age 3 years hence = 21 + 3 = 24 years.
∴ The correct answer is 24 yrs.
Alternate Method
Given:
Calculations:
⇒ From (3), S = P ÷ 3
⇒ From (1), R = P − 12
⇒ Substitute R and S in (2):
⇒ ((P − 12) + 8) ÷ (P ÷ 3) = 17 ÷ 7
⇒ (P − 4) ÷ (P ÷ 3) = 17 ÷ 7
⇒ 3 × (P − 4) ÷ P = 17 ÷ 7
⇒ 21 × (P − 4) = 17P
⇒ 21P − 84 = 17P
⇒ 4P = 84
⇒ P = 21 years (Present age)
⇒ Age after 3 years = 21 + 3 = 24 years
∴ The correct answer is 24 yrs.
Additional Information
Ratio and Proportion in Ages
When the ratio of ages at different time intervals is given, always equate the constant difference or express all variables in terms of a single variable.
Age Difference Property
The difference between the ages of two persons remains constant throughout their lives, regardless of the number of years passed.
Future and Past Ages
If present age is 'x', age 'n' years hence is (x + n) and age 'n' years ago was (x − n).
The compound interest on a certain sum of money for 2 years is Rs. 2,781 and the simple interest for the same time at the same rate is Rs. 2,700. Find the rate of interest.
12%
8%
6%
3%
10%
Correct answer
6%
Why this answer is correct
Shortcut Trick
For 2 years, the difference between CI and SI is the interest earned on the first year SI.
SI for 1 year = 2700 ÷ 2 = ₹1350.
Difference (CI − SI) = 2781 − 2700 = ₹81.
Rate of Interest = (Difference ÷ 1st Year SI) × 100 = (81 ÷ 1350) × 100 = 6%.
∴ The correct answer is 6%.
Alternate Method
Given:
Simple Interest (SI) for 2 years = ₹2,700
Compound Interest (CI) for 2 years = ₹2,781
Time (T) = 2 years
Calculations:
⇒ SI for 1 year = 2700 ÷ 2 = ₹1,350
⇒ Difference (D) = CI − SI = 2781 − 2700 = ₹81
⇒ This difference ₹81 is the interest calculated on the first year's interest (₹1,350) for 1 year.
⇒ Rate (R) = (D × 100) ÷ (SI for 1 year × 1)
⇒ R = (81 × 100) ÷ 1350
⇒ R = 8100 ÷ 1350 = 6%
∴ The correct answer is 6%.
Additional Information
Relation between CI and SI for 2 years
The ratio of Compound Interest to Simple Interest for 2 years is given by the formula: CI / SI = (200 + R) / 200.
Difference formula for 2 years
The difference (D) between CI and SI for 2 years is D = P × (R/100)2.
Compound Interest Basics
For the first year (if compounded annually), Simple Interest and Compound Interest are always equal.
Ram, Lakhan and Bharat started a business with capital ₹ 85000, ₹ 68000 and ₹ 34000 respectively. At the end of 5 years, the total Profit is 13,310. What is the difference of profit share between Ram and Bharat?
Rs. 3,630
Rs. 3,600
Rs. 3,500
Rs. 2,420
None of these
Correct answer
Rs. 3,630
Why this answer is correct
Shortcut Trick
The ratio of Profit Share is equal to the ratio of Investment when the time period is the same for all partners.
Ratio of Capitals (Ram : Lakhan : Bharat) = 85000 : 68000 : 34000 = 85 : 68 : 34 = 5 : 4 : 2.
Total ratio units = 5 + 4 + 2 = 11 units. Total Profit = Rs. 13,310.
Value of 1 unit = 13310 ÷ 11 = Rs. 1,210.
Difference between Ram and Bharat = (5 − 2) units = 3 units.
Difference in Profit = 3 × 1210 = Rs. 3,630.
∴ The correct answer is Rs. 3,630.
Alternate Method
Given: Ram's Capital = Rs. 85,000, Lakhan's Capital = Rs. 68,000, Bharat's Capital = Rs. 34,000. Total Profit = Rs. 13,310. Time = 5 years (constant).
Formula: Profit Ratio = (C1 × T1) : (C2 × T2) : (C3 × T3)
⇒ Ratio of Profit = (85000 × 5) : (68000 × 5) : (34000 × 5)
⇒ Ratio of Profit = 85 : 68 : 34 = 5 : 4 : 2
⇒ Let Ram's share = 5x, Lakhan's = 4x, Bharat's = 2x
⇒ 5x + 4x + 2x = 13310 ⇒ 11x = 13310 ⇒ x = 1210
⇒ Difference (Ram − Bharat) = 5x − 2x = 3x
⇒ 3 × 1210 = 3630
∴ The correct answer is Rs. 3,630.
Additional Information
Partnership Basics
In a partnership, profit is distributed based on the product of Investment and Time. If time is constant, profit depends solely on the investment ratio.
Simple vs Compound Partnership
A Simple Partnership involves investments for the same duration, while a Compound Partnership involves investments for different time periods.
Directions: The following line graph shows the number of projects completed in six different months by a company.
The total number of projects completed in January is approximately what percentage more/less than the total number of projects completed in March?
68%
77%
76%
71%
73%
Correct answer
71%
Why this answer is correct
Solution:
Number of projects completed in January = 120
Number of projects completed in March = 70
Required percentage = 120/70 × 100 = (171.14 - 100) ~ 71%
∴ The total number of projects completed in January is approximately 71% more than the total number of projects completed in March.
Directions: The following line graph shows the number of projects completed in six different months by a company.
If the total number of projects completed by company B in February is 50% more than that of company A (consider the above diagram for company A) in January and the sum of the total number of projects completed by company B in February and March is 255, then find the difference between the total number of projects completed by company B in February and March.
135
125
105
110
115
Correct answer
105
Why this answer is correct
Solution:
Number of projects completed by company A in January = 120
Number of projects completed by company B in February = 120 × 150/100 = 180
Number of projects completed by company B in March = 255 - 180 = 75
Required difference = (180 - 75) = 105
Directions: The following line graph shows the number of projects completed in six different months by a company.
Find the ratio of the total number of projects completed in May to the total number of projects completed in January and June together.
3: 7
2: 3
4: 5
2: 5
3: 5
Correct answer
2: 5
Why this answer is correct
Solution:
Number of projects completed in May = 100
Number of projects completed in January and June = (120 + 130) = 250
Required ratio = 100: 250 = 2: 5
Directions: The following line graph shows the number of projects completed in six different months by a company.
If the average number of projects completed in January, May and December is 115, then the total number of projects completed in February is what percentage of the total number of projects completed in December?
82%
84%
88%
92%
86%
Correct answer
88%
Why this answer is correct
Solution:
Number of projects completed in May = 100
Number of projects completed in January = 120
Number of projects completed in December = 115 × 3 - (100 + 120) = 125
Number of projects completed in February = 110
Required percentage = 110/125 × 100 = 88%
Directions: The following line graph shows the number of projects completed in six different months by a company.
If the total number of projects completed in August is twice the difference between the total number of projects completed in March and June, and the ratio of the total number of projects completed in April to July is 7: 5, then find the sum of the total number of projects completed in July and August.
265
350
220
240
250
Correct answer
220
Why this answer is correct
Solution:
Number of projects completed in March = 70
Number of projects completed in June = 130
Total number of projects completed in August = 2 × (130 - 70) = 120
Number of projects completed in April = 140
Number of projects completed in July = 140/7 × 5 = 100
Required sum = (120 + 100) = 220
If the principal of ₹ 10,000 amounts to ₹ 19,600 with 40% p.a. rate of interest compounded annually. Calculate the time for which it was invested.
10 years
5 years
2 years
4 years
3 years
Correct answer
2 years
Why this answer is correct
Shortcut Trick
Ratio of Amount (A) to Principal (P) is 19600 : 10000 = 196 : 100.
Rate is 40%, so the Multiplier is (1 + 40/100) = 1.4 or 14/10.
Check the power: (14/10)2 = 196/100.
Since the power is 2, the Time Period is 2 years.
∴ The correct answer is 2 years.
Alternate Method
Given: Principal (P) = ₹ 10,000, Amount (A) = ₹ 19,600, Rate (R) = 40% p.a.
Formula Used: A = P(1 + R/100)n
⇒ 19600 = 10000(1 + 40/100)n
⇒ 19600 / 10000 = (140 / 100)n
⇒ 196 / 100 = (1.4)n
⇒ (1.4)2 = (1.4)n
⇒ n = 2
∴ The correct answer is 2 years.
Additional Information
Compound Interest (CI) Formula
Interest is calculated on the initial principal and also on the accumulated interest of previous periods: CI = A − P.
Half-yearly Compounding
If interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n) in the formula.
Rule of 72
A quick way to estimate the time required to double an investment: Time ≈ 72 ÷ Interest Rate.
Ramesh purchased a land for Rs. 45000 and sold (3/5) part at a loss of 5%. How much per cent of profit should be sold the remaining part so that he made 15% profit on the whole?
45%
35%
50%
55%
40%
Correct answer
45%
Why this answer is correct
Shortcut Trick
Use the weighted average method based on parts of the land.
Let the total parts be 5. Loss is taken as negative and profit as positive.
Total Profit = (Part 1 × P/L%) + (Part 2 × P/L%)
15% × 5 = (3 × −5%) + (2 × x%)
75 = −15 + 2x ⇒ 2x = 90 ⇒ x = 45%.
∴ The correct answer is 45%.
Alternate Method
Given: Total CP = Rs. 45,000, Loss on 3/5 part = 5%, Total Profit required = 15%.
Formulas: SP = CP × (100 ± P/L)% / 100 | Profit = SP − CP.
⇒ Total required SP = 45000 × (115/100) = Rs. 51,750.
⇒ CP of 3/5 part = 45000 × (3/5) = Rs. 27,000.
⇒ SP of 3/5 part (at 5% loss) = 27000 × (95/100) = Rs. 25,650.
⇒ Required SP for remaining part = 51750 − 25650 = Rs. 26,100.
⇒ CP of remaining 2/5 part = 45000 × (2/5) = Rs. 18,000.
⇒ Profit on remaining part = 26100 − 18000 = Rs. 8,100.
⇒ Profit % = (8100 / 18000) × 100 = 45%.
∴ The correct answer is 45%.
Additional Information
Weighted Average in Profit & Loss
When different portions of a single quantity are sold at different profit/loss percentages, the overall profit/loss percentage is the weighted average of individual percentages.
Independent of Actual Value
If the question asks for the percentage profit or loss, the actual price (like Rs. 45000) does not affect the final result; only the ratio of parts matters.
What will come in the place of the question mark ‘?’ in the following question?
\(2\frac{1}{4} + 3\frac{1}{6} - 1\frac{2}{8} = ?; + 1\frac{1}{{12}}\)
\(4{3 \over 12}\)
\(3{4 \over 24}\)
\(3{1 \over 12}\)
\(3{5 \over 12}\)
\(3{4 \over 12}\)
Correct answer
\(3{1 \over 12}\)
Why this answer is correct
Calculation:
Given expression is-
\(2\frac{1}{4} + 3\frac{1}{6} - 1\frac{2}{8} = ?; + 1\frac{1}{{12}}\)
First convert mixed fraction into proper fraction
(9/4) + (19/6) – (10/8) = ? + (13/12)
⇒ ? = 9/4 + 19/6 – 10/8 – 13/12
⇒ ? = (54 + 76 – 30 – 26)/24
⇒ ? = 74/24 = 37/12 = \(3{1 \over 12}\)
\(2\frac{1}{4} + 3\frac{1}{6} - 1\frac{2}{8} = ?; + 1\frac{1}{{12}}\)
⇒ (2 + 3 - 1 - 1) + (1/4 + 1/6 - 2/8 - 1/12)
⇒ 3 + (1/12)
⇒ \(3{1 \over 12}\)
What will come in the place of the question mark ‘?’ in the following question?
\(1{1\over6} + {1\over8} + {2{5\over8}} - {3{2\over3}} = ?\)
1/5
2/3
1/6
1/4
1/2
Correct answer
1/4
Why this answer is correct
Given:
\(1{1\over6} + {1\over8} + {2{5\over8}} - {3{2\over3}} = ?\)
Concept Used:
Calculation:
\(1{1\over6} + {1\over8} + {2{5\over8}} - {3{2\over3}} = ?\)
⇒ 1 + 2 - 3 + [(1/6) + (1/8) + (5/8) - (2/3)] = ?
⇒ (1/6) + (1/8) + (5/8) - (2/3) = ?
⇒ (6/8) - (1/2) = ?
⇒ ? = 1/4
∴ The value of (?) is 1/4.
What will come in place of question mark (?) in the following question?
58 + (222 ÷ 3) ÷ 37 + 22 = ?2
9
4
8
6
7
Correct answer
8
Why this answer is correct
Concept Used:
Calculation:
⇒58 + (222 ÷ 3) ÷ 37 + 22 = ?2
⇒ 58 + 74/37 + 4 = ?2
⇒ 58 + 2 + 4 = ?2
⇒ 64 = ?2
⇒ 8 = ?
What will come in the place of the question mark ‘?’ in the following question?
250 ÷ 5 × 2/350 + 26/7 = ?
5
6
7
4
none of these
Correct answer
4
Why this answer is correct
Concept:
Calculation:
⇒ 250 ÷ 5 × 2/350 + 26/7 = ?
⇒ 50 × (2/350) + 26/7 = ?
⇒ 2/7 + 26/7 = ?
⇒ 28/7 = ?
⇒ ? = 4
∴ The required result will be 4.
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.