In a textile shop, the number of shirts having a design is thrice the number of shirts not having a design. The shop also has sarees of exactly three colours − Brown, Black and Yellow. The number of brown sarees is half the number of black sarees and one-fifth of the number of yellow sarees. Find the number of shirts not having a design, given that the total number of shirts and sarees in the shop is 72 and the number of sarees that are handspun is four times that of those that are not handspun
Question
In a textile shop, the number of shirts having a design is thrice the number of shirts not having a design. The shop also has sarees of exactly three colours − Brown, Black and Yellow. The number of brown sarees is half the number of black sarees and one-fifth of the number of yellow sarees. Find the number of shirts not having a design, given that the total number of shirts and sarees in the shop is 72 and the number of sarees that are handspun is four times that of those that are not handspun
Solution
The problem can be solved by setting up a system of equations based on the information given in the problem.
Let's denote:
- Sd as the number of shirts with a design
- Sn as the number of shirts without a design
- B as the number of brown sarees
- Bl as the number of black sarees
- Y as the number of yellow sarees
- H as the number of handspun sarees
- N as the number of non-handspun sarees
From the problem, we have the following equations:
-
Sd = 3*Sn (The number of shirts having a design is thrice the number of shirts not having a design)
-
B = 0.5Bl and B = 0.2Y (The number of brown sarees is half the number of black sarees and one-fifth of the number of yellow sarees)
-
H = 4*N (The number of sarees that are handspun is four times that of those that are not handspun)
-
Sd + Sn + B + Bl + Y = 72 (The total number of shirts and sarees in the shop is 72)
From equation 1, we can express Sd in terms of Sn: Sd = 3Sn
Substitute Sd in equation 4, we get: 3Sn + Sn + B + Bl + Y = 72, which simplifies to 4Sn + B + Bl + Y = 72
From equation 2, we can express B in terms of Bl and Y: B = 0.5Bl = 0.2Y
Substitute B in the above equation, we get: 4Sn + 0.5Bl + Bl + 0.2Y + Y = 72, which simplifies to 4Sn + 1.5Bl + 1.2Y = 72
From equation 3, we can express H in terms of N: H = 4N
Substitute H in equation 4, we get: Sd + Sn + B + Bl + Y + 4N = 72, which simplifies to 3Sn + Sn + 0.5Bl + Bl + 0.2Y + 4N = 72
Solving the system of equations, we get: Sn = 8, Sd = 24, B = 8, Bl = 16, Y = 40, H = 48, N = 12
So, the number of shirts not having a design is 8.
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