A thread is marked into three parts whose lengths are in the ratio 2:5:6. Two types of knots A and B reduce the length of the thread by different lengths. On the first part, 6 knots of type A are made, on the second part 10 knots of type B are made and on the third part, 5 knots of type A and 5 knots of type B are made. After this, the lengths of the three parts taken in the same order, are in the ratio of 1 : 7 : 8. What is the ratio of the reduction in length due to knot A to that of knot B?
a) 3 : 5
b) 4 : 5
c) 5 : 4
d) 5 : 3

• d) 5:3
  let 2x,5x,6x be the original length of the respective parts. let P and Q be the lengths reduced by knot A and B respectively. hence new lengths are 2x-6P,5x-10Q,6x-(5P+5Q), but given that new ratios are 1:7:8. hence 2x-6P/5x-10Q=1/7,
  2x-6P/6x-(5P+5Q)=1:8. solve these two for value of x in terms of P and Q. we must finally find the ratio of P/Q.
• 11 years agoHelpfull: Yes(10) No(1)