(a) green balls = 4, Yellow balls = 3, black balls =  5.
so, Black balls
(b) 5 parts of Black balls = 40 balls
\(\therefore \) 1 part of Black balls = \(\frac{40}{5}=8 \text { balls }\)
4part of Green balls = 4 \(\times\) 8 = 32
3 part of yellow balls = 3 \(\times\) 8 = 24
If there are 40 black balls, then total number of balls = 32 + 24 + 40 = 96 balls
(c) Number of green balls = 32
Number of Yellow balls = 24

Ratio of red beads: blue beads = 35: 30
Fraction of 35 : 30  \(=\frac{35}{30}\)
= 7:6
Also given that the bracelet made is smaller in size
∴ The possible ways are red beads: blue beads
The equivalent ways are
\( \frac{7 \times 2}{6 \times 2}=\frac{14}{12}=14: 12 \)
\( \frac{7 \times 3}{6 \times 3}=\frac{21}{18}=21: 18 \)
\( \frac{7 \times 4}{6 \times 4}=\frac{28}{24}=28: 24\)
= 7 : 6 (or) 14: 12 (or) 21 : 18 (or) 28 : 24
In 4 different way can she made.

Run rate = Ratio of runs to overs
Run rate of Karmegam = \(\frac { 54 }{ 9 } \) = \(\frac { 6 }{ 1 } \) = 6 :1
Run rate of Asif = \(\frac { 77 }{ 11 } \) = \(\frac { 7 }{ 1 } \) = 7 :1
∴ Asif's run rate is better.

The given pictures are in the ratio 2 : 5 and 4 : 3 respectively.
Here the extremes are 2 and 3 and the means are 5 and 4.
Product of extremes, ad = 2 \(\times\)3 = 6.
Product of means, bc = 5 \(\times\) 4 = 20.
Thus, we find ad\(\neq\)  bc and hence 2 : 5 and 4 : 3 are not in proportion.

(i) For Provisions:
Dividing the total amount Rs. 4000 into 3 + 2 = 5 equal parts then
3 out of 5 parts are spent for provisions & 2 out of 5 parts for vegetables
\(\therefore 4000\times\frac{3}{5}=2400\) for provisions
(ii) For vegetables:
\(4000\times\frac{2}{5}=1600\) for Vegetables
\(\therefore\) Rs.2400 spend on provisions & Rs.1600 spend on Vegetables