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
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Important Questions from Problem Solving
Six numbers, 7, 8, 9, 10, 11 and 12 are written on different faces of a dice. Three positions of this dice are shown here. Find the number on the face opposite 12.
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
Rahul invests his savings, which is Rs. 25,000 in his bank that pays 7 per cent annual interest. How much will he earn by way of interest in one year?
Which two signs need to be interchanged to make the following equation correct? 5 × 4 + 12 - 3 ÷ 6 = 18
In a company there are 3 departments - IT, HR and Help Desk. In the IT department there are 125 employees and in the HR department the number of employees is 1/5th of IT. The helpdesk department has 20 employees less than total employees in IT and HR together. What is the total number of employees working in all three departments?
