Question
The HCF of two numbers is 21 and their LCM is 693. If
one of the numbers is 63, find the other number and verify that it is a multiple of the HCF.Solution
For two numbers a and b: a × b = HCF × LCM Let other number = x. 63 × x = 21 × 693 Compute RHS: 21×693 = 21×(700 − 7) = 14,700 − 147 = 14,553 So x = 14,553 / 63 63×200 = 12,600 Remaining: 1,953 63×30 = 1,890 Remaining: 63 So x = 200 + 30 + 1 = 231 Check: 231 ÷ 21 = 11, So 231 is a multiple of the HCF.
‘P’ and ‘Q’ invested Rs. (x + 300) and Rs. (x – 500) respectively in a business for 2 months and 4 months. If P’s share of the profit is Rs....
A invest twice the sum invested by B and withdraws half of sum after 4 months and again withdraws half of the remaining sum after 6 months. Find ratio o...
P started a business with an investment of Rs.15000, after 6 months Q joined him with Rs.18000 and after another 6 months R joined them with Rs.20000. I...
Two firms, X and Y, began a joint venture by investing in a ratio of 9:16. After six months, Firm Y withdrew its entire investment. At the end of the ye...
The contributions made by A and B are in the ratio of 6:5. If 12% of total profit is donated and A gets 1320 as his share of profit, what is the total p...
Armaan and Bittu invested Rs. 32,000 and Rs. 20,000, respectively, into a business for 6 months and 8 months, respectively. If th...
M and N started a partnership with investments of Rs. 10,000 and Rs. 8,000. After 6 months, M increased his contribution by Rs. 2,000 and O joined with ...
A man invests ₹40,000 in a business. After 3 years, he sells 40% of his stake for a 30% profit and reinvests the amount. After another 2 years, he sel...
A invested Rs X in a scheme. After 6 months, B joined with Rs 3000 more than that of A. After an year, ratio of profit of B to the total profit was 5: 9...
A, B and C invest in a business as follows, A invests ₹40,000 for 12 months, B invests ₹60,000 for 9 months, C invests ₹80,000 for 6 months. If th...
