Model 2 Formula method ‘M1D1W1 = M2D2W2’ Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on time & work topic of quantitative aptitude

Questions : The average wage of 500 workers was found to be Rs.200. Later on, it was discovered that the wages of two workers were misread as 180 and 20 instead of 80 and 220. The correct average wage is :

(a) Rs.200.10

(b) Rs.200.20

(c) Rs.201.00

(d) Rs.200.50

The correct answers to the above question in:

Answer: (b)

Total wages of 500 workers

= 500 × 200 = Rs.100000

Now, according to question,

Correct Average

= ${(100000 - 180 - 20 + 80 + 220)}/500$

= $100100/500$ = Rs.200.20

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Read more formula method m1d1w1 m2d2w2 Based Quantitative Aptitude Questions and Answers

Question : 1

A can do a work in 12 days while B can do it in 15 days. They undertake to complete it together for Rs.450. what will be the share of A in this amount of money ?

a) Rs.200

b) Rs.240

c) Rs.300

d) Rs.250

Answer: (d)

Ratio of A’s and B’s 1 day’s work

= $1/12 : 1/15$ = 15 : 12 = 5 : 4

Sum of the terms of ratio

= 5 + 4 = 9

A’s share

= Rs.$(5/9 × 450)$ = Rs.250

Question : 2

A, B and C can work together for Rs. 550. A and B together are to do $7/11$ of the work. The share of C should be

a) Rs.200

b) Rs.300

c) Rs.450

d) Rs.400

Answer: (a)

Part of work done by C

= $1 - 7/11 = 4/11$

Total amount received = Rs.550

C’s share

= Rs.$(4/11 × 550)$ = Rs.200

Question : 3

A, B and C are employed to do a piece of work for Rs.575. A and C are supposed to finish $19/23$ of the work together. Amount shall be paid to B is

a) Rs.210

b) Rs.100

c) Rs.475

d) Rs.200

Answer: (b)

Work done by B

= $1 - 19/23 = {23 - 19}/23 = 4/23$

(A + C) : B = $19/23 : 4/23$ = 19 : 4

Sum of ratios = 19 + 4 = 23

B’s share = $4/23 × 575$ = Rs.100

Question : 4

A and B undertake a piece of work for Rs. 250. A alone can do that work in 5 days and B alone can do that work in 15 days. With the help of C, they finish the work in 3 days. If every one gets paid in proportion to work done by them, the amount C will get is :

a) Rs.50

b) Rs.100

c) Rs.200

d) Rs.150

Answer: (a)

Let C alone complete the work in x days.

According to the question,

$1/5 + 1/15 + 1/x = 1/3$

$1/x = 1/3 - 1/5 - 1/15$

= ${5 - 3 - 1}/15 = 1/15$

x = 15 days = Time taken by C alone.

Ratio of the 1 day’s work of A, B and C

= $1/5 : 1/15 : 1/15$ = 3 : 1 : 1

Sum of the terms of ratio

= 3 + 1 + 1 = 5

C’s share

= Rs.$(1/5 × 250)$ = Rs.50

Question : 5

Two men undertook to do a job for Rs.1400. One of them can do it alone in 7 days, and the other in 8 days. With the assistance of a boy they together completed the work in 3 days. How much money will the boy get ?

a) Rs.300

b) Rs.325

c) Rs.250

d) Rs.275

Answer: (d)

Using Rule 25,

First man’s 1 day’s work = $1/7$

Second man’s 1 day’s work = $1/8$

Let, Boy’s 1 day’s work = $1/x$

$1/7 + 1/8 + 1/x = 1/3$

$1/x = 1/3 - 1/7 - 1/8$

= ${56 - 24 - 21}/168 = 11/168$

Ratio of their one day’s work

= $1/7 : 1/8 : 11/168$ = 24 : 21 : 11

Sum of the ratios

= 24 + 21 + 11= 56

Boy’s share in wages

= $11/56 × 1400$ = Rs.275

Question : 6

A and B undertook to do a piece of work for Rs.4500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of the money is

a) Rs.2250

b) Rs.1500

c) Rs.375

d) Rs.750

Answer: (d)

Using Rule 25
If A, B and C finish the work in m, n and p days respectively and they receive the total wages R, then the ratio of their wages is $1/m : 1/n : 1/p$

C’s 1 day’s work

= $1/4 - (1/8 + 1/12) = 1/4 - ({3 + 2}/24)$

= $1/4 - 5/24 = {6 - 5}/24 = 1/24$

A : B : C = $1/8 : 1/12 : 1/24$ = 3 : 2 : 1

C’s share = Rs.$(1/6 × 4500)$ = Rs.750

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