Let the number be 10x + y. Then x + y = 9 and 9(10x + y) = 2(10y + x). The second simplifies to 88x – 11y = 0, giving y = 8x. Substituting yields x = 1, y ...
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Let their present ages be x and y. Then x – 5 = 3(y – 5) and x + 10 = 2(y + 10). Simplifying yields x – 3y = -10 and x – 2y = 10. Solving gives y ...
Let the fraction be x/y. The conditions form (x+1)/(y-1) = 1 and x/(y+1) = 1/2, yielding x – y = -2 and 2x – y = 1. Subtracting gives x = 3 and y = 5. The fraction is 3/5. Cbse ...
Extend PQ so QS = PQ. By SAS, △APQ ≅ △CSQ, making CS = AP = PB and CS ∥ PB. Thus PBCS is a parallelogram, giving PQ ∥ BC and PQ = BC/2. For (ii), complete PBCS similarly to ...
No, they do not have to be midpoints. In a parallelogram ABCD, choosing points dividing opposite sides in equal ratios (like AP = CR = 1/3 AB and BQ = DS = 1/3 BC) creates an inscribed parallelogram that is ...