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Of three positive numbers, the ratio of the first and second numbers is 3:4 & that of the second and third numbers is 5:6. The product of the second and third numbers is 4320. What is the sum of three numbers?

Correct Answer: 177

Let the second & third numbers are 2x & 3x respectively. ATQ, 5x*6x = 4320 30*x*x = 4320 x*x = 144 x=12 Hence, second number = 5x = 5*12 = 60 Third number = 6x = 6*12 = 72 Ratio of first & second number = ¾ Hence, first number = ( ¾)*60 = 45 Sum of these 3 numbers = 60+72+45 = 177

Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right

Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$m + AB) = determinant ($$I$$n + BA), where $$I$$k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right

Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right

Of three positive numbers, the ratio of first and second is 8 : 9, that of second and third is 3 : 4. The product of first and third is 2400. The sum of the three number is = ?

Of the three numbers, the sum of the first two is 55, sum of the second and third is 65, and sum of third with thrice of the first is 110. The third number is -

দুটি সংখ্যার অনুপাত ৫ঃ৬ অনুপাত ৫ঃ৬ এবং তাদের গ.সা.গু ৪ হলে, চোট সংখ্যাটি কত?

Of the three number, the sum of the first two is 73, the sum of the second and the third is 77 and the sum of the third and thrice the first is 104. The third number is ?

The sum of the eigen values of the matrix given below is \[\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 1&5&1 \\ 3&1&1 \end{array}} \right

The product of eigen values of the matrix P is \[{\text{P}} = \left[ {\begin{array}{*{20}{c}} 2&0&1 \\ 4&{ - 3}&3 \\ 0&2&{ - 1} \end{array}} \right

In a 4-digit number, the sum of the first two digits is equal to that of last two digits. The sum of the first and last digits is equal to third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?