Mangoes Problem: Step-by-Step Solution
This solution addresses the quantitative reasoning problem concerning the number of mangoes eaten by five children.
Define Variables and Formulate Equations
Let the number of mangoes eaten by each child be denoted by their respective initials (A, B, C, D, E). We translate the given information into algebraic equations:
- A ate 8 mangoes less than B: \( A = B - 8 \)
- C and E together ate 37 mangoes: \( C + E = 37 \)
- D ate 8 mangoes more than C: \( D = C + 8 \)
- B ate 5 mangoes more than C: \( B = C + 5 \)
- B and A together ate 40 mangoes: \( B + A = 40 \)
Calculate Mangoes Eaten
Solve the system of equations to find the number of mangoes eaten by each child:
- Find B and A: Substitute the first equation into the fifth equation.
\( B + (B - 8) = 40 \)
\( 2B - 8 = 40 \)
\( 2B = 48 \)
\( B = 24 \)
Now, find A using \( A = B - 8 \): \( A = 24 - 8 = 16 \). - Find C: Use the value of B in the fourth equation.
\( 24 = C + 5 \)
\( C = 24 - 5 \)
\( C = 19 \) - Find D: Use the value of C in the third equation.
\( D = 19 + 8 \)
\( D = 27 \) - Find E: Use the value of C in the second equation.
\( 19 + E = 37 \)
\( E = 37 - 19 \)
\( E = 18 \)
The calculated number of mangoes are: A=16, B=24, C=19, D=27, E=18.
Verify Statements
Compare the calculated values with the given statements:
- Statement 1: E ate 18 mangoes and C ate 19 mangoes. (Correct, matches E=18, C=19)
- Statement 2: C ate 11 mangoes and B ate 16 mangoes. (Incorrect, C=19, B=24)
- Statement 3: D ate 19 mangoes and C ate 27 mangoes. (Incorrect, D=27, C=19)
- Statement 4: A ate 24 mangoes and B ate 16 mangoes. (Incorrect, A=16, B=24)
The statement "E ate 18 mangoes and C ate 19 mangoes" is confirmed by the calculations.
Similar Questions
- Read the given paragraph and answer the question.
There are five persons A, G, M, J and D. Every person has to select one item each from a box containing items numbered from 1 to 5. A and J selected items 5 and 2 respectively. G cannot select item 3, while M cannot select item 3 or 5.
Which item can G select? - Read the given information carefully and answer the question that follows.
- There are four persons: P, Q, R and S.
- One of them is a doctor and plays football and cricket.
- P and Q are teachers.
- P plays badminton.
- The lawyer and both the teachers are swimmers.
- One of them also plays tennis.
- S plays carrom and is a lawyer.
- All the four persons play two games each and follow one profession.
The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the fourth equation on the same basis:
$7 \blacksquare 4 = 27/4$
$6 \blacksquare 1 = 5$
$4 \blacksquare 3 = 11/3$
$a \blacksquare b = ?$- Four girls, Radha, Neena, Mohita and Jyoti, are to be served in a sequence by a service provider. However, there are some limitations as follows: Mohita and Jyoti cannot be served one after the other; Neena cannot be served at the third number in sequence; and Radha and Neena are to be served one after the other. Considering the given information, which of the following statements is compulsorily true?
- In a school there were 6 teachers. A and B taught Hindi and English. D and A taught Mathematics and Science. C and E taught English and Mathematics. F and B taught Hindi and French. Who taught the maximum number of subjects?
- Huma's mother gave Huma 4 baskets of blueberries each labelled A, B, C, D. Each berry weighs 5 g, except for the basket, which has all rotten berries, where each berry has a weight of 3 g. Huma took out 1, 2, 3 and 4 berries from the baskets A, B, C and D respectively and weighed them to be 44 grams. Which basket has the rotten berries?
- In a test paper, correct answers fetch three marks and there is a penalty of one mark for each wrong answer. A student who attempts 76 questions gets 144 marks. How many questions did the student get right?
- In a test series, South Africa defeated England twice, Bangladesh defeated South Africa twice, England defeated Bangladesh twice, South Africa defeated Pakistan twice and Bangladesh defeated Pakistan twice. Which country lost the highest number of times?
Important Questions from Problem Solving
- A cyclist starting from point $X$ travels straight towards east for 3km and then turns right and covers 4km and reaches point $Y$. What is the shortest distance between point $X$ and $Y$?
- Read the given paragraph and answer the question.
There are five persons A, G, M, J and D. Every person has to select one item each from a box containing items numbered from 1 to 5. A and J selected items 5 and 2 respectively. G cannot select item 3, while M cannot select item 3 or 5.
Which item can G select? - Read the given information carefully and answer the question that follows.
- There are four persons: P, Q, R and S.
- One of them is a doctor and plays football and cricket.
- P and Q are teachers.
- P plays badminton.
- The lawyer and both the teachers are swimmers.
- One of them also plays tennis.
- S plays carrom and is a lawyer.
- All the four persons play two games each and follow one profession.
The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the fourth equation on the same basis:
$7 \blacksquare 4 = 27/4$
$6 \blacksquare 1 = 5$
$4 \blacksquare 3 = 11/3$
$a \blacksquare b = ?$- Four girls, Radha, Neena, Mohita and Jyoti, are to be served in a sequence by a service provider. However, there are some limitations as follows: Mohita and Jyoti cannot be served one after the other; Neena cannot be served at the third number in sequence; and Radha and Neena are to be served one after the other. Considering the given information, which of the following statements is compulsorily true?
