untitled

which one is right of the above speech? (a) i and ii (b) i and iii (c) ii and iii (d) i, ii and iii Answer the questions 5 – 6 f ...

0DWK,;;)RUPD Chapter Eleven Algebraic Ratio and Proportion It is important for us to have a clear concept of ratio and pr ...

In the above figure, let the base of two triangles be aandb respectively and their height is h unit. If the areas of the triangl ...

i.e.,b:a d:c (2) If a:b c:dthena:c b:d [alternendo] Proof : Given that, d c b a ?ad bc [multiplying both the sides by bd] or, cd ...

Therefore, c d d d c d a b b b a b  u   u  [multiplying (i) and (ii)] i.e.,. c d c d a b a b     [ here azbandczd] (6) I ...

25 2 21 16 or, b b or, 5 b 50 ?b 10 Putting b 10 in equation (iii), we get, a 35 ? The present age of father is 35 years, and t ...

Example 5. Solve : 1 , 0 2 2. 1 1 1 1 b a b bx bx ax ax        Solution : Given that, 1 1 1 1 1     bx bx ax ax ax ax ...

Solution : Given that, x a b 6 1 1  ? 6 ab (ab)x[multiplying both the sides by abx] i.e., ( ) 6 a b ab x  or, a b b a x  2 3 ...

2 1 2 1 2 1 2 1 1 1 1 1 or, 2 2 2 2                 p p p p p p p p x x x x [by componendo - dividendo] 1 0. 2 2 ...

0DWK,;;)RUPD or, ( ) 0       b c d a d a b c a c or, (ac)(dabc) 0 ? Either ac 0 i.e.,a c or, abcd 0. Exampl ...

Exercise 11⋅ 1 If the sides of two squares be a and b metres respectively, what will be the ratio of their areas? If the area o ...

(i) 3 3 3 3 3 3 3 3 c d b c b c a b     (^) (ii) (a^2 b^2 c^2 )(b^2 c^2 d^2 ) (abbccd)^2 If a b ab x  4 , show that ...

earning : Sami’s earning = 1500 : 2500 = 3 : 5. Hence, Roni’s : Soni’s : Sami’s earning = 2 : 3 : 5. If two ratios are of the fo ...

Solution : Let each side of the square be a metre ? Area of the square be a^2 square metre If the side increases by 10%, each si ...

Example 15. Divide Tk. 5100 among 3 persons in such a way that 1st person’s part : 2nd person’s part : 3rd person’s part are 9 1 ...

On the basis of above information, which one of the followings is correct? (a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) ...

In a cricket game, the total runs scored by Sakib, Mushfique and Mashrafi were 171. The ratio of runs scored by Sakib and Mushf ...

0DWK,;;)RUPD (b) Determine the area of a square drawn with the diagonal of a rectangle taking greater side as length and ...

Chapter Twelve Simple Simultaneous Equations with Two Variables For solving the mathematical problems, th e most important topic ...

Value of x Value of y Value of L.H.S. ( 2x + y) R.H.S. .... 5 3 0  2 ..... 2 6 12 16 ..... 12 10 2 12 6 6 12 0 12 12 4 16 12  ...