1.

Direction: P, Q and R started a business by investing Rs. 1200, Rs. 2000 and Rs. 2400 respectively. After a quarter, they invested amounts in the ratio 1 : 4 : 2. After another quarter, they invested amounts in the ratio 3 : 2 : 3. In the last quarter, the ratio of investments was same as in 2nd quarter. Also, in the last quarter, the respective amounts of P, Q and R were double than the respective amounts invested in 2nd quarter. The total investment of R before 4th quarter was Rs. 1800 more than that of P during same duration. Also, the ratio of R’s share in profit to total profit at the end of year was 69 : 206. Also, they withdrew the amount after each quarter.Find the total amount of investment done by P, Q and R.1). Rs. 206002). Rs. 184003). Rs. 242004). Rs. 15600

Answer»

<P>? The ratio of investments in 2nd quarter was 1 : 4 : 2,

∴ Suppose the amounts were Rs. x, Rs. 4x and Rs. 2x;

? The ratio of investments in 3rd quarter was 3 : 2 : 3,

∴ Suppose the amounts were Rs. 3y, Rs. 2y and Rs. 3y;

In last quarter, respective amounts are double than the AMOUNT invested in 2nd quarter;

∴ Suppose the amounts were Rs. 2x, Rs. 8x and Rs. 4x;

ACCORDING to the given condition:

Total investment of R before 4th quarter was Rs. 1800 more than that of P during same duration;

∴ (2400 + 2x + 3y) = 1800 + (1200 + x + 3y)

⇒ 2400 + 2x = 3000 + x

⇒ x = Rs. 600

Now, ratio of profit SHARE:

A : B : C = (1200 × 3 + x × 3 + 3y × 3 + 2x × 3) : (2000 × 3 + 4x × 3 + 2y × 3 + 8x × 3) : (2400 × 3

+ 2x × 3 + 3y × 3 + 4x × 3)

⇒ (1200 + 3x + 3y) : (2000 + 12x + 2y) : (2400 + 6x + 3y)

Putting x = 600;

⇒ 3000 + 3y : 9200 + 2y : 6000 + 3y

? The ratio of R’s share in profit to total profit at the end of year was 69 : 206;

∴ (6000 + 3y) : (18200 + 8y) = 69 : 206

⇒ 1236000 + 618y = 1255800 + 552y

⇒ 66y = 19800

⇒ y = 300

∴ Total investment = 18200 + 8y

Putting y = 300

∴ Total investment = 18200 + 2400 = Rs 20600


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