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

(1) Given:

Value of second property = ₹ 60,00,000

Ratio (Priya : Seema) = $\dfrac{1}{5} : \dfrac{1}{7}$

Let us find L.C.M. of 5 and 7:

$\begin{array}{l|rr} 5 & 5, & 7 \ \hline 7 & 1, & 7 \ \hline & 1, & 1 \end{array}$

L.C.M. = 5 x 7 = 35

Priya : Seema = $(\dfrac{1}{5} \times 35) : (\dfrac{1}{7} \times 35)$

Priya : Seema = 7 : 5

Total parts = 7 + 5 = 12

Value of 1 part = ₹ 60,00,000 ÷ 12 = ₹ 5,00,000

Priya's amount = 7 parts x ₹ 5,00,000 = ₹ 35,00,000

Hence, option 4 is the correct option.

(2) Given:

Value of first property = ₹ 38,00,000

Ratio (Priya : Seema) = 7 : 12

Total parts = 7 + 12 = 19

Value of 1 part = ₹ 38,00,000 ÷ 19 = ₹ 2,00,000

Seema's amount = 12 parts x ₹ 2,00,000 = ₹ 24,00,000

Hence, option 2 is the correct option.

(3)

Calculate total for Priya.

From 1st property:

Ratio (Priya : Seema) = 7 : 12 $\quad$Given

Value of 1 part = ₹ 2,00,000 $\quad$[From previous step]

∴ 7 x 2,00,000 = ₹ 14,00,000

From 2nd property:

Priya's amount = ₹ 35,00,000 $\quad$[From step 1]

Total = ₹ 14,00,000 + ₹ 35,00,000 = ₹ 49,00,000

Calculate total for Seema.

From 1st property:

Seema's amount = ₹ 24,00,000 $\quad$[From step 2]

From 2nd property:

Ratio (Priya : Seema) = $\dfrac{1}{5} : \dfrac{1}{7}$

L.C.M. of 5 and 7 is 35.

Priya : Seema = $(\dfrac{1}{5} \times 35) : (\dfrac{1}{7} \times 35)$

Priya : Seema = 7 : 5

Value of 1 part = ₹ 5,00,000

∴ 5 x ₹ 5,00,000 = ₹ 25,00,000

Total = ₹ 24,00,000 + ₹ 25,00,000 = ₹ 49,00,000

Difference = Priya - Seema

= ₹ 49,00,000 - ₹ 49,00,000 = ₹ 0

Hence, option 1 is the correct option.

(4)

Seema's 1st amount = ₹ 24,00,000 $\quad$[From step 2]

Seema's 2nd amount = ₹ 25,00,000 $\quad$[From previous step]

Ratio = 24,00,000 : 25,00,000

Ratio = 24 : 25

Hence, option 3 is the correct option.