A scooter dealer bought an old bike listed at rs.24000 and got two successive discounts of 5% and 10%. He spends some amount on its gaining 6%. Find the amount spent by shopkeeper on repairs.
a)2000 b)2150
c)2480 d)2580
Answers
(95/100 *90/100 (24000) +repair) * 106/100 =24000
The complete question with the correct set of options is : A scooter dealer bought an old bike listed at Rs. 24,000 and got two successive discount of 5% and 10%. He spends some amount on its repair, and sells the bike at a price by gaining 6% on the listed price. Find the amount spent by the shopkeeper on repair.
a) Rs. 2000 b) Rs. 2150 c) Rs. 3480 d) Rs. 2580
SOLUTION :
The shopkeeper spent Rs. 3480 on the repair of the bike. Hence, option (c) is correct.
• Given,
Listed price or marked price of the old bike = Rs. 24,000
First discount (d1) = 5 %
Second discount (d2) = 10 %
• Selling price of an article with two successive discount is given by the formula :
S.P. = (1 - d1 / 100) (1 - d2 / 100) × Marked Price
• Now, price at which the bike was bought by the scooter dealer = (1 - 5 / 100) (1 - 10 / 100) × Rs. 24,000
=> C.P. = (1 - 0.05) (1 - 0.1) × Rs, 24,000
=> C.P. = 0.95 × 0.9 × Rs. 24,000
=> C.P. = Rs. 20, 520
• Let the amount spent on repairing the bike be x.
Therefore, total C.P. of the bike for the dealer = Rs. 20, 520 + x
• Profit % earned by the dealer = 6 % on M.P.
Therefore, S.P. of the bike = M.P. + 6 % of M.P.
=> S.P. = Rs. 24,000 + (6 / 100) × Rs. 24,000
= Rs. 24,000 + Rs. 1440
= Rs. 25, 440
• Now, the formula for the S.P. of an article is given as [ (100 + Gain %) / 100 ] × C.P.
• Putting S.P. as Rs. 25, 440 , gain as 6 % , and C.P. as Rs. 20, 520 + x in the above formula, we get,
Rs. 25, 440 = [ (100 + 6) / 100 ] × (Rs. 20, 520 + x)
=> Rs. 25, 440 = (106 / 100) × (Rs. 20, 520 + x)
=> (Rs. 25, 440 × 100) / 106 = Rs. 20, 520 + x
=> Rs. 24,000 = Rs. 20, 520 + x
=> x = Rs. 24, 000 - Rs. 20, 520
=> x = Rs. 3480
∴ The amount spent on the repair of the bike = Rs. 3480.