Write true (T) or false (F) :

(i) If a, b, c, d are in proportion, then ac = bd.

(ii) If a : b : : c : d, then a, b, c, d are said to be in absolute proportion.

(iii) If a, b, c, are in continued proportion, then the mean proportion b = $\dfrac{a + c}{2}$.

(iv) If x is the third proportional to a, b, then a : b : : b : x.

(v) 1, 2, 3, 4, are in proportion.

Ram Nath sold one of his properties worth ₹ 38,00,000. He wished to divide this money between his two daughters Priya and Seema in the ratio 7 : 12. He sold another property for ₹ 60,00,000. He divided this money between Priya and Seema in the ratio $\dfrac{1}{5} : \dfrac{1}{7}$

(1) What amount did Priya receive from the sale of second property ?

1. ₹ 14,00,000
2. ₹ 24,00,000
3. ₹ 25,00,000
4. ₹ 35,00,000

(2) What amount did Seema receive from the sale of first property ?

1. ₹ 14,00,000
2. ₹ 24,00,000
3. ₹ 25,00,000
4. ₹ 49,00,000

(3) The difference between the total amounts received by Priya and Seema is :

1. ₹ 0
2. ₹ 1,00,000
3. ₹ 2,00,000
4. ₹ 5,00,000

(4) The ratio between the amounts received by Seema from the sale of the first and the second properties is :

1. 1 : 1
2. 12 : 7
3. 24 : 25
4. 14 : 35

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

Assertion: The numbers 4, 8, 16 are in continued proportion.

Reason: Three numbers a, b, c are in continued proportion, if a : b = b : c.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.