Find real questions from previous competitive exam papers with answers and solutions.
Browse complete papersFind the wrong term in the following series.
205 , 236 , 279 , 304 , 341
205
236
279
304
341
Correct answer
279
Why this answer is correct
Given:
205 , 236 , 279 , 304 , 341
Calculation:
Here the logic follows as,
Hence, 279 is the wrong term
\(\therefore\) The correct answer is 279.
Direction: Given below are two quantities named A and B. Based on the given information you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: A car covers a distance of 1260 km in 18 hours. The average speed of a train is 6/7th times the average speed of the car. Find the distance covered by the train in the same time.
Quantity B: A 320 m long train crosses a tunnel thrice its length in 32 sec. What is the distance covered by the train in 8 hours?
Quantity A > Quantity B
Quantity A < Quantity B
Quantity A ≥ Quantity B
Quantity A ≤ Quantity B
Quantity A = Quantity B or No relation
Correct answer
Quantity A < Quantity B
Why this answer is correct
Quantity A:
Distance covered by the train in the same time = 1260 × 6/7 = 1080 km
Quantity B:
A 320 m long train crosses a tunnel thrice its length in 32 sec
⇒ Speed of the train = (320 + 320 × 3) /32 = 40 m/s
⇒ Distance covered by the train in 8 hours = 40 × 8 × 18/5 = 1152 km
∴ Quantity A < Quantity B
Direction: Given below are three quantities. Based on the given information, determine the Relation between the two quantities.
Quantity I: Present age of Rohit is 11 years more than the six times of the present age of his grandson Sunny and Sunny is 9 years younger to Prateek whose age is 19 years old. Find the present age of Rohit.
Quantity II: Average age of the remaining persons in the group, if the average age of a group of 12 persons is 30 years. Two persons, each 25 years old, left the group.
Quantity I > Quantity II
Quantity I < Quantity II
Quantity I ≥ Quantity II
Quantity I ≤ Quantity II
Quantity I = Quantity II
Correct answer
Quantity I > Quantity II
Why this answer is correct
Quantity I:
Age of grandson = 19 – 9 = 10 years
Age of Rohit = 10 × 6 + 11 = 71 years
Quantity II:
Required average \(= \frac{{12; \times ;30 - 2; \times ;25}}{{10}}\)
= \(\frac{{360 - 50}}{{10}}\)
= 31 years
∴ Quantity I > Quantity II
Directions: Study the information carefully and answer the questions.
Rajat and Suman jointly acquired a 6-acre fruit orchard in the ratio of 4:2 in the year 2020 and began cultivating apples in the year 2021. In that year, Rajat, being the primary investor, gave 60 kg of apples, which was 10% of his total production for that year, to Suman. As a result, Suman's total apple quantity increased by 30%. In the year 2022, Suman's total apple production was 50% more than the previous year, so he returned 20% of his total apples produced quantity to Rajat. After receiving from Suman, Rajat's total apple quantity increased by 15%. In the year 2023, both had produced an equal quantity of apples, and Rajat's production of apples was increased by 20% over the total quantity of apples he had produced in the previous year.
If the apple price is ₹50 per kg in 2021 and increases by 10% each subsequent year, what is the total revenue earned by Suman over the 3 years (assume that Suman sold his apples after the transactions)?
₹48,530
₹59,810
₹55,240
₹52,450
None of these
Correct answer
₹55,240
Why this answer is correct
General Solution:
Orchard Area Division
Total land = 6 acres
Rajat : Suman = 4 : 2 ⇒ 2 : 1
Apple Production in 2021:
Let Rajat's production = R₁ kg
He gave 60 kg to Suman, which was 10% of his production
⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg
Suman got 60 kg which increased his total by 30%
⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg
2021: Rajat = 600 kg, Suman = 200 kg
2022 Production:
Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg
He gives 20% of 300 = 60 kg to Rajat
Let Rajat's 2022 own production = R₂
Total apples with Rajat = R₂ + 60 = 15% more than R₂
⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15
⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg
2022: Rajat = 400 kg, Suman = 300 kg
2023 Production:
Both produced equal quantities
Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg
⇒ So, Suman’s 2023 production = 480 kg
2023: Rajat = 480 kg, Suman = 480 kg
Thus:
| Year | Rajat (kg) | Suman (kg) |
|---|---|---|
| 2021 | 600 | 200 |
| 2022 | 400 | 300 |
| 2023 | 480 | 480 |
Calculations:
Apple prices per year:
2021: ₹50 per kg
2022: ₹50 + 10% = ₹55 per kg
2023: ₹55 + 10% = ₹60.5 per kg
Suman's final apple quantity each year
2021: He had 200 kg + 60 kg from Rajat = 260 kg
2022: Produced 300 kg – gave 60 kg to Rajat = 240 kg
2023: Produced = 480 kg
Calculate Revenue for each year:
2021: 260 kg × ₹50 = ₹13,000
2022: 240 kg × ₹55 = ₹13,200
2023: 480 kg × ₹60.5 = ₹29,040
Total Revenue = 13,000 + 13,200 + 29,040 = ₹55,240
Thus, the correct answer is ₹55,240.
Directions: Study the information carefully and answer the questions.
Rajat and Suman jointly acquired a 6-acre fruit orchard in the ratio of 4:2 in the year 2020 and began cultivating apples in the year 2021. In that year, Rajat, being the primary investor, gave 60 kg of apples, which was 10% of his total production for that year, to Suman. As a result, Suman's total apple quantity increased by 30%. In the year 2022, Suman's total apple production was 50% more than the previous year, so he returned 20% of his total apples produced quantity to Rajat. After receiving from Suman, Rajat's total apple quantity increased by 15%. In the year 2023, both had produced an equal quantity of apples, and Rajat's production of apples was increased by 20% over the total quantity of apples he had produced in the previous year.
What was the ratio of Rajat's total apples (own production + received) to Suman's total apples (after giving) in 2022?
17:9
15:8
19:10
23:12
None of these
Correct answer
23:12
Why this answer is correct
General Solution:
Orchard Area Division
Total land = 6 acres
Rajat : Suman = 4 : 2 ⇒ 2 : 1
Apple Production in 2021:
Let Rajat's production = R₁ kg
He gave 60 kg to Suman, which was 10% of his production
⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg
Suman got 60 kg which increased his total by 30%
⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg
2021: Rajat = 600 kg, Suman = 200 kg
2022 Production:
Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg
He gives 20% of 300 = 60 kg to Rajat
Let Rajat's 2022 own production = R₂
Total apples with Rajat = R₂ + 60 = 15% more than R₂
⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15
⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg
2022: Rajat = 400 kg, Suman = 300 kg
2023 Production:
Both produced equal quantities
Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg
⇒ So, Suman’s 2023 production = 480 kg
2023: Rajat = 480 kg, Suman = 480 kg
Thus:
| Year | Rajat (kg) | Suman (kg) |
|---|---|---|
| 2021 | 600 | 200 |
| 2022 | 400 | 300 |
| 2023 | 480 | 480 |
Calculations:
2022 Apple Quantities:
Rajat's own production in 2022 = 400 kg
He received 60 kg from Suman
Total apples with Rajat = 400 + 60 = 460 kg
Suman's production = 300 kg
He gave 20% of 300 = 60 kg to Rajat
Total apples left with Suman = 300 − 60 = 240 kg
Required Ratio:
⇒ Rajat : Suman = 460 : 240 ⇒ 23 : 12
Thus, the correct answer is 23 : 12.
Directions: Study the information carefully and answer the questions.
Rajat and Suman jointly acquired a 6-acre fruit orchard in the ratio of 4:2 in the year 2020 and began cultivating apples in the year 2021. In that year, Rajat, being the primary investor, gave 60 kg of apples, which was 10% of his total production for that year, to Suman. As a result, Suman's total apple quantity increased by 30%. In the year 2022, Suman's total apple production was 50% more than the previous year, so he returned 20% of his total apples produced quantity to Rajat. After receiving from Suman, Rajat's total apple quantity increased by 15%. In the year 2023, both had produced an equal quantity of apples, and Rajat's production of apples was increased by 20% over the total quantity of apples he had produced in the previous year.
If in 2024, both Rajat and Suman decide to increase their production by the average annual percentage increase from 2021 to 2023, what would be the approximate total production in 2024?
1056 kg
1200 kg
1120 kg
1000 kg
None of these
Correct answer
1056 kg
Why this answer is correct
General Solution:
Orchard Area Division
Total land = 6 acres
Rajat : Suman = 4 : 2 ⇒ 2 : 1
Apple Production in 2021:
Let Rajat's production = R₁ kg
He gave 60 kg to Suman, which was 10% of his production
⇒ 10% of R₁ = 60 ⇒ R₁ = 600 kg
Suman got 60 kg which increased his total by 30%
⇒ 60 = 30% of S₁ ⇒ S₁ = 200 kg
2021: Rajat = 600 kg, Suman = 200 kg
2022 Production:
Suman's 2022 production = 50% more than 2021 = 200 + 50% of 200 = 300 kg
He gives 20% of 300 = 60 kg to Rajat
Let Rajat's 2022 own production = R₂
Total apples with Rajat = R₂ + 60 = 15% more than R₂
⇒ R₂ + 60 = R₂ + 15% of R₂ = R₂ × 1.15
⇒ R₂ + 60 = 1.15R₂ ⇒ 60 = 0.15R₂ ⇒ R₂ = 400 kg
2022: Rajat = 400 kg, Suman = 300 kg
2023 Production:
Both produced equal quantities
Rajat's 2023 production is 20% more than previous year = 400 + 20% of 400 = 480 kg
⇒ So, Suman’s 2023 production = 480 kg
2023: Rajat = 480 kg, Suman = 480 kg
Thus:
| Year | Rajat (kg) | Suman (kg) |
|---|---|---|
| 2021 | 600 | 200 |
| 2022 | 400 | 300 |
| 2023 | 480 | 480 |
Calculations:
2021 total = 600 (Rajat) + 200 (Suman) = 800 kg
2023 total = 480 + 480 = 960 kg
Change over 2 years = 960 − 800 = 160 kg
Average annual % increase = [(Final − Initial)/Initial] ÷ 2 × 100
⇒ (960 − 800)/800 × 100 = 20% over 2 years ⇒ Annual average = 10%
2024 projection = 960 × (1 + 10/100) = 960 × 1.10 = 1056 kg
∴ Approximate total production in 2024 = 1056 kg
Income of 'P' is 60% more than expenditure of 'Q' and 150% more than savings of 'R'. Expenditure of P:Q:R = 4:5:4. If income of Q = 3 × expenditure of R, difference between savings of P and R = Rs. 1,600, find savings of Q.
Rs. 14,000
Rs. 14,400
Rs. 12,000
Rs. 12,800
Rs. 10,400
Correct answer
Rs. 14,000
Why this answer is correct
Shortcut Trick
Let Expenditure of P, Q, R be 4x, 5x, 4x respectively.
Income of P = 1.6 × 5x = 8x. Savings of R = 8x ÷ 2.5 = 3.2x.
Savings of P = Income P − Exp P = 8x − 4x = 4x.
Difference (Savings P − R) = 4x − 3.2x = 0.8x = ₹1,600 ⇒ x = 2000.
Income of Q = 3 × 4x = 12x. Savings of Q = 12x − 5x = 7x = 7 × 2000 = ₹14,000.
∴ The correct answer is ₹14,000.
Alternate Method
Given: Ratio of Expenditures P:Q:R = 4:5:4. Let they be 4x, 5x and 4x.
Formula: Savings = Income − Expenditure
⇒ Income of P = 160% of Expenditure of Q = 1.6 × 5x = 8x
⇒ Savings of R: Income of P is 150% more (i.e., 250%) than Savings of R
⇒ 8x = 2.5 × Savings of R ⇒ Savings of R = 8x ÷ 2.5 = 3.2x
⇒ Savings of P = Income of P − Expenditure of P = 8x − 4x = 4x
⇒ Difference in Savings (P and R) = 4x − 3.2x = 0.8x
⇒ 0.8x = 1600 ⇒ x = 2000
⇒ Income of Q = 3 × Expenditure of R = 3 × 4x = 12x
⇒ Savings of Q = Income of Q − Expenditure of Q = 12x − 5x = 7x
⇒ Savings of Q = 7 × 2000 = ₹14,000
∴ The correct answer is ₹14,000.
Additional Information
Income-Expenditure Relation
The fundamental relation used in these problems is Income = Expenditure + Savings.
Percentage Increase
If a value is A% more than B, then the value is (100 + A)% of B or (1 + A/100) × B.
Ratio Balancing
When multiple components (Income, Exp) are linked across different people, expressing all terms in a single variable (x) simplifies the comparison.
P, Q and R started a business by investing ₹60,000, ₹80,000 and ₹x respectively. P invested for 12 months, Q invested for 9 months and R invested for 8 months. If P receives 30% of the total profit, find the initial investment of R.
₹90,000
₹100,000
₹110,000
₹120,000
₹130,000
Correct answer
₹120,000
Why this answer is correct
Given:
P invested = ₹60,000 for 12 months
Q invested = ₹80,000 for 9 months
R invested = ₹x for 8 months
P's share in profit = 30%
Calculation:
⇒ Profit ratio is proportional to Investment × Time
⇒ P's investment unit
= 60,000 × 12 = 7,20,000
⇒ Q's investment unit
= 80,000 × 9 = 7,20,000
⇒ R's investment unit = 8x
⇒ According to the question,
7,20,000/(7,20,000 + 7,20,000 + 8x) = 30/100
⇒ 7,20,000/(14,40,000 + 8x) = 3/10
⇒ 72,00,000 = 43,20,000 + 24x
⇒ 28,80,000 = 24x
⇒ x = ₹1,20,000
A boat covers 48 km downstream in 3 hours and 30 km upstream in 3 hours. Find the speed of the boat in still water.
12 km/h
13 km/h
14 km/h
15 km/h
16 km/h
Correct answer
13 km/h
Why this answer is correct
Given:
Downstream distance = 48 km
Downstream time = 3 hours
Upstream distance = 30 km
Upstream time = 3 hours
Calculation:
⇒ Downstream speed = 48 ÷ 3 = 16 km/h
⇒ Upstream speed = 30 ÷ 3 = 10 km/h
⇒ Speed of boat in still water = (16 + 10)/2 = 26/2 = 13 km/h
Final Answer = 13 km/h
The present age ratio of A and B is 5 : 7, while the present age ratio of A and C is 5 : 9. Four years from now, the sum of the ages of B and C will be 88 years. Find the present age of A.
22 years
25 years
27 years
35 years
30 years
Correct answer
25 years
Why this answer is correct
Given:
Ratio of A : B = 5 : 7
Ratio of A : C = 5 : 9
After 4 years, the sum of the ages of B and C = 88 years
Calculation:
⇒ Let the present age of A = 5x
⇒ Present age of B = 7x
⇒ Present age of C = 9x
⇒ According to the question,
(7x + 4) + (9x + 4) = 88
⇒ 16x + 8 = 88
⇒ 16x = 80
⇒ x = 5
⇒ Present age of A = 5 × 5 = 25 years
Final Answer = 25 years