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What will come in place of question mark...

What will come in place of question mark (?) in the following questions.
`(5599)/(1331) xx (3773)/(2036) xx (88)/(49) = ? - 6^(2)`

A

52

B

51

C

50

D

53

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \((5599)/(1331) \times (3773)/(2036) \times (88)/(49) = ? - 6^2\), we will follow these steps: ### Step 1: Calculate \(6^2\) First, we need to calculate \(6^2\): \[ 6^2 = 36 \] ### Step 2: Simplify the left-hand side of the equation Now we will simplify the left-hand side of the equation: \[ \frac{5599}{1331} \times \frac{3773}{2036} \times \frac{88}{49} \] ### Step 3: Factor and cancel common terms We will look for common factors in the fractions to simplify them. 1. **Simplifying \(\frac{5599}{1331}\)**: - Both numbers can be divided by 11. - \(5599 \div 11 = 509\) - \(1331 \div 11 = 121\) So, \(\frac{5599}{1331} = \frac{509}{121}\). 2. **Simplifying \(\frac{3773}{2036}\)**: - Again, both numbers can be divided by 11. - \(3773 \div 11 = 343\) - \(2036 \div 11 = 185\) So, \(\frac{3773}{2036} = \frac{343}{185}\). 3. **Simplifying \(\frac{88}{49}\)**: - This fraction cannot be simplified further. Now we can rewrite the left-hand side: \[ \frac{509}{121} \times \frac{343}{185} \times \frac{88}{49} \] ### Step 4: Combine the fractions Now we will multiply the numerators and denominators: \[ \frac{509 \times 343 \times 88}{121 \times 185 \times 49} \] ### Step 5: Calculate the numerator and denominator Calculating the numerator: - \(509 \times 343 = 174,607\) - \(174,607 \times 88 = 15,366,536\) Calculating the denominator: - \(121 \times 185 = 22,385\) - \(22,385 \times 49 = 1,095,865\) So we have: \[ \frac{15,366,536}{1,095,865} \] ### Step 6: Simplify the fraction Now we will simplify \(\frac{15,366,536}{1,095,865}\). After performing the division: \[ \frac{15,366,536}{1,095,865} \approx 14 \] ### Step 7: Set up the equation Now we can set up the equation: \[ 14 = ? - 36 \] ### Step 8: Solve for ? To find the value of \(?\): \[ ? = 14 + 36 = 50 \] ### Final Answer Thus, the value that comes in place of the question mark (?) is: \[ \boxed{50} \]
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ADDA247-NUMBER SYSTEM, SIMPLIFICATION AND APPROXIMATION -PRELIMS QUESTIONS (LEVEL - 1)
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