Page 16 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

Solution
The initial ratio is 4 : 3.
Let ‘k’ be the common ratio.
=> Initial quantity of colored water = 3 k
=> Final quantity of sugar solution = 4 k
=> Final quantity of colored water = 3 k + 5
Final ratio = 4 K + 15 6
2
=> k = 3 3 =
7
Therefore, the initial quantity of sugar solution in the given mixture = 4 k = 12 liters
Q 6. Two friends Hari and Ram started a business with an initial capital contribution of Rs. 2 lac and Rs. 3 lacs.
At the end of the year, the business made a profit of Rs. 40,000. Find the share of each in the profit.
Solution:
We know that if the time period of investment is the same, profit/loss is divided by the ratio of the value of the
investment.
=> Ratio of value of investment of Hari and Ram = 2,00,000 :3,00,000 = 2 :3
=> Ratio of share in profit = 2 :3
=> Share of Hari in profit = (2/5) x 40,000 = Rs. 16,000
=> Share of Ram in profit = (3/5) x 40,000 = Rs. 24,000
Q 7. There are three friends A, B, and C started a business, each investing Rs. 20,000. After 5 months A withdrew
Rs. 5000, B withdrew Rs. 4000 and C invested Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900
was recorded. Find the share of each.
Solution
We know that if the period of investment is not constant, the gains/losses from the business are divided in the
ratio of their inputs, where input is calculated as the product of an amount of investment and the time period of
investment.
So, input = value of investment x period of investment, and here, the period of investment would be broken into
parts as the investment is not constant throughout the time period.
A’s input = (20,000 x 5) + (15,000 x 7) = 20,5000
B’s input = (20,000 x 5) + (16,000 x 7) = 2,12,000
C’s input = (20,000 x 5) + (26,000 x 7) = 2,82,000
=> A : B : C = 20,500 : 2,12,000 : 2,82,000

=> A : B : C = 205 : 212 : 282 643 − = − 8 60
6 −
=
4
3 −
8
=> A : B : C = (205/ 699) : (212 / 699) : (282/ 699) = Rs.30
4
8
60
=
2
8
4
Thus, A’s share = (205/ 699) x 69900 = Rs. 20,5000 = 2 = Rs.30
8
4
3 −
6 −
60
=
3
9
6
B’s share = (212 / 699) x 69900 = Rs. 21200 = 2 = Rs.30
3 +
8
4
=
=
9
3 +
6
12
4
8
C’s share = (282/ 699) x 69900 = Rs. 28200 3 x = 50 × 30 = 10teeth
4 +
=
=
Example 3 + 6 4 + 8 3 12 4 180 x = 50 × 30 = 10teeth
9
= = 180

50
4
8
• A steel plate of 800 x 1400 mm is to be drawn to a scale of 1:20. What will be the lengths in the Fig 1.
12
4 +
1 x = × 30 = 10teeth
180
The reduction ratio is . 1 x = 70 × 2.5 = 25days
20 70 × 2.5
B is reduced from 800 to 800 x = 40 mm. 7 x = = 25days
1 20 7

1
L is reduced from 1400 x = 70 mm. Δh x = 70 × 2.5 = 25days

1
=
20
40mm
=
800 ×
1
Δh
7
l
20

• Find the number of teeth of the larger gear in the gear transmission shown in the Fig 2.
1
=
20
=
800 ×
40mm
Speed ratio = 400 : 300 1 20 Δh 1 l 20

800 1 × = 40mm =
Teeth ratio = 24:T = 20 70mm l 20
1400 ×
20 1400 × 1 = 70mm
1 20
1400 × = 70mm 3
400 T 20
= CITS : WCS - Mechanical - Exercise 2
300 24 400 = T
T
400 300 24
24 × 400 =
24
T = 300 = 32Teeth
300 T = 24 × 400 = 32Teeth
24 × 400 300
120 T = 300 = 32Teeth
= 30gallons/ day
4 120 = 30gallons/ day
120 4
= 30gallons/ day
4