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Question
The difference between two selling prices of a shirt at profits of 4% and 5% is Rs 6. Find
(i) C.P. of the shirt
(ii) the two selling prices of the shirt
Solution
\[\text { Let the C . P of both the shirts be Rs . x } . \]
\[\text { C . P = Rs . x }\]
\[\text { For shirt 1 }: \]
\[\text { Profit is 4 % } : \]
\[\text { Profit % } = \frac{\text { Profit }}{CP} \times 100\]
\[\text { Profit } = \frac{4}{100} \times C . P\]
\[ = Rs . 0 . 04x\]
\[\text { S . P = C . P + Profit }\]
\[ = x + 0 . 04x\]
\[ = Rs . 1 . 04x\]
\[\text { For shirt 2: } \]
\[\text { Profit = 5 % : } \]
\[\text { C . P = Rs . x }\]
\[\text { Profit = } \frac{5}{100} \times C . P\]
\[ = Rs . 0 . 05x\]
\[S . P = C . P + Profit\]
\[ = x + 0 . 05x\]
\[ = \text { Rs .} 1 . 05x\]
\[\text { It is given that the difference between their profits is Rs } . 6\]
\[\text { So, }1 . 05x - 1 . 04x = 6\]
\[0 . 01x = 6\]
\[x = Rs . 600\]
\[\text { Thus, C . P = Rs } . 600\]
\[\text { S . P of shirt 1 } = Rs . 1 . 04x\]
\[ = \text { Rs }. 1 . 04 \times 600\]
\[ = Rs . 624\]
\[\text { S . P of shirt 2 = Rs } . 1 . 05x\]
\[ =\text { Rs . 1 . 05 }\times 600\]
\[ = \text { Rs } . 630 .\]
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Match the entries in Column I with the appropriate entries in Column II:
| Column I | Column II |
| (i) 3:5 | (A) ₹ 54 |
| (ii) 2.5 | (B) ₹ 47 |
| (iii) 100% | (C) ₹ 53 |
| (iv) `2/3` | (D) ₹ 160 |
| (v) `6 1/4%` | (E) 60% |
| (vi) 12.5% | (F) 25% |
| (vii) SP when CP = ₹ 50 and loss = 6 % | (G) `1/16` |
| (viii) SP when CP = ₹ 50 and profit = ₹ 4 | (H) 250% |
| (ix) Profit% when CP = ₹ 40 and SP = ₹ 50 | (I) ₹ 159 |
| (x) Profit% when CP = ₹ 50 and SP = ₹ 60 | (J) `66 2/3%` |
| (xi) Interest when principal = ₹ 800, Rate of interest = 10% per annum nd period = 2 years |
(K) 20% |
| (xii) Amount when principal = ₹ 150, Rate of interest = 6% per annum and period = 1 year |
(L) 0.125 |
| (M) 3:2 | |
| (N) ₹ 164 | |
| (O) 3:3 |
