Ranjan Singh makes statues of brass. Brass is an alloy of copper and zinc. Ranjan uses two varieties of brass for different kinds of statues. Variety 1 contains copper and zinc mixed in the ratio 7 : 4 and variety 2 contains these metals in the ratio 5 : 3. Ranjan makes an elephant statue from variety 1 and a horse statue from variety 2. The elephant statue weighs 176 g and it is known that the brass used in the horse statue contains 135 g zinc.

(1) Find the quantity of copper present in the brass used to make the elephant statue.

1. 98 g
2. 112 g
3. 121 g
4. 132 g

(2) How much copper is contained in the brass used to make the horse statue ?

1. 165 g
2. 175 g
3. 205 g
4. 225 g

(3) How much zinc is contained in the brass used to make the two statues ?

1. 169 g
2. 179 g
3. 189 g
4. 199 g

(4) The ratio of the quantities of copper and zinc used to make the two statues is :

1. 113 : 98
2. 337 : 148
3. 221 : 199
4. 337 : 199

(1) Given:

Elephant statue is made from variety 1.

Variety 1 ratio (Copper : Zinc) = 7 : 4

Total weight of statue = 176 g

Total parts = 7 + 4 = 11

Value of 1 part = 176 g ÷ 11 = 16 g

Copper = 7 parts x 16 g = 112 g

Hence, option 2 is the correct option.

(2) Given:

Horse statue is made from variety 2.

Variety 2 ratio (Copper : Zinc) = 5 : 3

Quantity of Zinc = 135 g

3 parts of Zinc = 135 g

Value of 1 part = 135 g ÷ 3 = 45 g

Copper = 5 parts x 45 g

Copper = 225 g

Hence, option 4 is the correct option.

(3) Given:

Zinc in Horse = 135 g

Zinc in Elephant:

Variety 1 ratio (Copper : Zinc) = 7 : 4

Value of 1 part = 16 g $\quad$[From step 1]

∴ 4 parts x 16 g = 64 g

Zinc in Elephant = 64 g

Total Zinc = 135 g + 64 g = 199 g

Hence, option 4 is the correct option.

(4)

Calculate Copper in Elephant:

Variety 1 ratio (Copper : Zinc) = 7 : 4

Value of 1 part = 16 g $\quad$[From step 1]

Copper in Elephant = 7 x 16 g = 112 g

Copper in Horse = 225 g $\quad$[From step 2]

Total Copper = Copper in Elephant + Copper in Horse

Total Copper = 112 g + 225 g = 337 g $\quad$[Substituting the values]

Total Copper = 337 g

Total Zinc = 199 g $\quad$[From previous step]

The ratio of the quantities of copper and zinc = 337 : 199

Hence, option 4 is the correct option.