Question

Directions: The question is given below consists of two statements. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.

Find the wages of P, Q and R together if they worked together to complete the work.

Statement 1. P, Q and R alone can complete the work in 12, 18 and 36 days respectively.

Statement 2. The sum of the wages of P and R is Rs. 640 

1.

Statement 1 alone is sufficient to answer the question but statement 2 alone is not sufficient. 

2.

Statement 2 alone is sufficient to answer the question but statement 1 alone is not sufficient. 

3.

Both statement 1 and statement 2 together is needed to answer the question.

4. Neither statement 1 and nor statement 2 is sufficient to answer the question. 
5. Either statement 1 alone or statement 2 alone is sufficient to answer the question. 

Answer 1

Correct Answer - Option 3 :

Both statement 1 and statement 2 together is needed to answer the question.

Given:

P, Q and R alone can complete the work in 12, 18 and 36 days respectively.

The sum of the wages of P and R is Rs. 640 

Formula used:

If a person does work in 'n' days then one day work is done by a person = 1/n part of total work.

The wage of a person is directly proportional to the efficiency of a person.

If A and B does work in x and y days respectively, the efficiency will be in the ratio of  y : x

Calculation:

The efficiency of P, Q and R will be (1/12) : (1/18) : (1/36)

LCM of (12, 18 and 36) = 36

Then the efficiency of P, Q and R will be in the ratio (1/12) × 36 : (1/18) × 36 : (1/36) × 36

⇒ 3 : 2 : 1

Let the efficiency of P, Q and R be 3k, 2k and k

According to the question,

3k + k = 640

⇒ 4k = 640

⇒ k = 640/4

⇒ k = 160

Now, the wage of P = 3k

⇒ 3 × 160

⇒ Rs. 480 

The wage of Q = 2k

⇒ 2 × 160

⇒ Rs. 320

The wage of R = k

⇒ Rs. 160

The wages of P, Q and R together = (480 + 320 + 160)

⇒ Rs. 960

∴ We can say that Both statement 1 and statement 2 together is needed to answer the question.