The DAV Class 7 Maths Solutions and DAV Class 7 Maths Chapter 5 Worksheet 3 Solutions of Application of Percentage offer comprehensive answers to textbook questions.
DAV Class 7 Maths Ch 5 WS 3 Solutions
Question 1.
I purchased a watch for ₹ 330 and sold it at a loss of 20%. Find S.P. of the watch.
Answer:
C.P. = ₹ 330, loss = 20%, S.P. = ?
S.P. = C.P. [1 – \(\frac{\text { loss }}{100}\)] = 330[1 – \(\frac{20}{100}\)]
= 300 × \(\frac{4}{5}\)
= 264
Question 2.
By selling a T.V. for ₹ 8000, a shopkeeper loses 20% of his cost. If he sells it for ₹ 11000, what profit or loss would be there for him?
Answer:
S.P. = T 8000, Loss = 20%, C.P. = ?
S.P. = C.P. (1 – \(\frac{\text { Loss }}{100}\))
8000 = C.P. × \(\frac{4}{5}\)
8000 = C.P. × \(\frac{20}{100}\)
C.P. = 8000 × \(\frac{4}{5}\) = ₹ 10,000
If S.P. = ₹ 11,000
∴ Profit = S.P. – C.P. = ₹ 11,000 – ₹ 10,000 = ₹ 1000
Hence the profit = ₹ 1000
Question 3.
A shopkeeper purchased a T.V. set for ₹ 9000 and sold it at a loss of 5%. Find the selling price of the T.V. Set.
Answer:
C.P. = ₹ 9000, loss = 5%, S.P. = ?
S.P = C.P[1 – \(\frac{\text { loss }}{100}\)]
= 9000(1 – \(\frac{5}{100}\))
= 9000 × \(\frac{19}{20}\)
= 450 × 19 = ₹ 8550
Hence S.P. = ₹ 8550
Question 4.
Seeta sells a dinning set to Neeta for ₹ 6000 and gains 20%, for how much should she sell it to increase her profit by another 5%?
Answer:
C.P. = ₹ 6000, gain 20%, S.P. = ?
S.P = C.P.(1 + \(\frac{\text { gain }}{100}\))
6000 = C.P. (1 + \(\frac{20}{100}\))
6000 = C.P. × \(\frac{6}{5}\)
C.P = 6000 × \(\frac{5}{6}\) = ₹ 5000
Profit = \(\frac{5}{100}\) × 5000 = ₹ 250
Total S.P. = ₹ 6000 + ₹ 250 = ₹ 6250
Question 5.
Ranjan bought a second hand scooter for ₹ 6000. He spent ₹ 300 on its repairs and sold it to vineet at a profit of 10%. Vineet sold the scooter to Mukesh at a loss of 10%. At what price did Mukesh buy the scooter?
Answer:
C.P. of Scooter for Ranjan = ₹ 6000
Money spent on repairing = ₹ 300
∴ Actual C.P. for Ranjan = ₹ 6000 + ₹ 300 = ₹ 6300
S.P. = C.P.( 1 +\(\frac{\text { Profit }}{100}\))
= 6300 (1 + \(\frac{10}{100}\)) = 6930
C.P. for Vineet = ₹ 6930
S.P. = C.P. (1 – \(\frac{\text { Loss }}{100}\)) = 6930 (1 – \(\frac{10}{100}\))
= 6930 × \(\frac{9}{10}\) = 6237
Hence Mukesh bought the scooter for ₹ 6237
Question 6.
A man buys two pens at ₹ 20 each. He sells one at a gain of 5% and other at a loss of 5%. Find his gain or loss %.
Answer:
C.P. of one pen = ₹ 20
gain = 5%
S.P = C.P.(1 + \(\frac{\text { gain }}{100}\))
= 20(1 × \(\frac{5}{100}\))
= 20 × \(\frac{21}{20}\)
= 21
C.P. of other pen = ₹ 20
loss = 5%
S.P. = C.P.(1 – \(\frac{\text { Loss }}{100}\))
= 20(1 – \(\frac{5}{100}\)) = 20 × \(\frac{19}{20}\) = ₹ 19
S.P. of the two pens = ₹ 21 + ₹ 19 = ₹ 40
C.P. of the two pens = ₹ 20 + ₹ 20 = ₹ 40
Hence there is no loss and no profit.
Question 7.
Mr. Tandon purchased a computer for ₹ 32000 and a microwave over for ₹ 6500. On computer, he lost 5% and on microwave he gained 15%. Find his total gain or loss percent.
Answer:
C.P. of a computer = ₹ 32000
C.P. of a microwave oven = ₹ 6500
For Computer, S.P = C.P(1 – \(\frac{\text { Loss }}{100}\)) = 32000(1 – \(\frac{5}{100}\))
= 32000 × \(\frac{19}{20}\)
= 1600 × 19
= ₹ 30400
For microwave oven, S.P = C.P.(1 + \(\frac{\text { gain }}{100}\))
= 6500(1 + \(\frac{15}{100}\))
= 6500 × \(\frac{23}{20}\)
= 325 × 23
= ₹ 7475
Combined C.P. = ₹ 32000 + ₹ 6500 = ₹ 38500
Combined S.P = ₹ 30400 + ₹ 7475 = ₹ 37875
C.P > S.P.
loss = ₹ 38500 – ₹ 37875 = ₹ 625
loss% = \(\frac{625 \times 100}{38500}=\frac{125}{77}\)% or 1\(\frac{48}{77}\)%
Hence the loss = 1\(\frac{48}{77}\)%
Question 8.
A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays ₹ 1500, what did A pay for it?
Answer:
S.P. of bicycle for B = C.P. for C = ₹ 1500
S.P. = C.P. (1 + \(\frac{\text { Profit }}{100}\))
1500 – C.P. (1 + \(\frac{25}{100}\))
1500 = C.P. × \(\frac{5}{4}\)
C.P = 1500 × \(\frac{4}{5}\)
C.P. = ₹ 1200
C.P. for B = S.P. for A
S.P. = C.P.(1 + \(\frac{\text { Profit }}{100}\))
1200 -C.P.(1 + \(\frac{20}{100}\))
1200 = C.P. × \(\frac{6}{5}\)
⇒ C.P. = 1200 × \(\frac{5}{6}\)
= ₹ 1000
Hence the money paid by A = ₹ 1000